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Spintronics: Fundamentals and applications
Igor Zˇutic´∗
Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park, College Park,
Maryland 20742-4111, USA
Jaroslav Fabian†
Institute for Theoretical Physics, Karl-Franzens University, Universita¨tsplatz 5, 8010 Graz, Austria
S. Das Sarma
Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park, College Park,
Maryland 20742-4111, USA
Spintronics, or spin electronics, involves the study of active control and manipulation of spin
degrees of freedom in solid-state systems. This article reviews the current status of this subject,
including both recent advances and well-established results. The primary focus is on the basic
physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-
polarized transport in semiconductors and metals. Spin transport differs from charge transport
in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The
authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various
theories of spin injection and spin-polarized transport are applied to hybrid structures relevant
to spin-based devices and fundamental studies of materials properties. Experimental work is
reviewed with the emphasis on projected applications, in which external electric and magnetic
fields and illumination by light will be used to control spin and charge dynamics to create new
functionalities not feasible or ineffective with conventional electronics.
Contents
I. Introduction 1
A. Overview 1
B. History and background 3
1. Spin-polarized transport and magnetoresistive effects3
2. Spin injection and optical orientation 6
II. Generation of spin polarization 7
A. Introduction 7
B. Optical spin orientation 9
C. Theories of spin injection 11
1. F/N junction 11
2. F/N/F junction 15
3. Spin injection through the space-charge region 17
D. Experiments on spin injection 18
1. Johnson-Silsbee spin injection 18
2. Spin injection into metals 20
3. All-semiconductor spin injection 21
4. Metallic ferromagnet/semiconductor junctions 24
III. Spin relaxation and spin dephasing 25
A. Introduction 25
1. T1 and T2 25
2. Experimental probes 27
B. Mechanisms of spin relaxation 28
1. Elliott-Yafet mechanism 28
2. D’yakonov-Perel’ mechanism 30
3. Bir-Aronov-Pikus Mechanism 35
4. Hyperfine-interaction mechanism 36
C. Spin relaxation in metals 37
∗Electronic address: igorz@physics.umd.edu. Present address:
Center for Computational Materials Science, Naval Research Lab-
oratory, Washington, D.C. 20375, USA
†Electronic address: jaroslav.fabian@uni.graz.at
D. Spin relaxation in semiconductors 39
1. Bulk semiconductors 40
2. Low-dimensional semiconductor structures 41
3. Example: spin relaxation in GaAs 42
IV. Spintronic devices and applications 46
A. Spin-polarized transport 46
1. F/I/S tunneling 46
2. F/I/F tunneling 48
3. Andreev reflection 50
4. Spin-polarized drift and diffusion 52
B. Materials considerations 53
C. Spin filters 56
D. Spin diodes 57
E. Spin transistors 60
1. Spin field-effect transistors 60
2. Magnetic bipolar transistor 61
3. Hot-electron spin transistors 62
F. Spin qubits in semiconductor nanostructures 64
V. Outlook 65
Acknowledgments 66
References 67
I. INTRODUCTION
A. Overview
Spintronics is a multidisciplinary field whose central
theme is the active manipulation of spin degrees of free-

2dom in solid-state systems.1 In this article the term spin
stands for either the spin of a single electron s, which
can be detected by its magnetic moment −gµBs (µB is
the Bohr magneton and g is the electron g factor, in a
solid generally different from the free electron value of
g0 = 2.0023), or the average spin of an ensemble of elec-
trons, manifested by magnetization. The control of spin
is then a control of either the population and the phase
of the spin of an ensemble of particles, or a coherent
spin manipulation of a single or a few-spin system. The
goal of spintronics is to understand the interaction be-
tween the particle spin and its solid-state environments
and to make useful devices using the acquired knowledge.
Fundamental studies of spintronics include investigations
of spin transport in electronic materials, as well as un-
derstanding spin dynamics and spin relaxation. Typical
questions that are posed are (a) what is an effective way
to polarize a spin system? (b) how long is the system
able to remember its spin orientation? (c) how can spin
be detected?
Generation of spin polarization usually means creating
a nonequilibrium spin population. This can be achieved
in several ways. While traditionally spin has been ori-
ented using optical techniques in which circularly polar-
ized photons transfer their angular momenta to electrons,
for device applications electrical spin injection is more de-
sirable. In electrical spin injection a magnetic electrode
is connected to the sample. When the current drives
spin-polarized electrons from the electrode to the sample,
nonequilibrium spin accumulates there. The rate of spin
accumulation depends on spin relaxation, the process of
bringing the accumulated spin population back to equi-
librium. There are several relevant mechanisms of spin
relaxation, most involving spin-orbit coupling to provide
the spin-dependent potential, in combination with mo-
mentum scattering providing a randomizing force. Typ-
ical time scales for spin relaxation in electronic systems
are measured in nanoseconds, while the range is from pico
to microseconds. Spin detection, also part of a generic
spintronic scheme, typically relies on sensing the changes
in the signals caused by the presence of nonequilibrium
spin in the system. The common goal in many spintronic
devices is to maximize the spin detection sensitivity to
the point it detects not the spin itself, but changes in the
spin states.
Let us illustrate the generic spintronic scheme on a
prototypical device, the Datta-Das spin field effect tran-
sistor (SFET) (Datta and Das, 1990), depicted in Fig. 1.
The scheme shows the structure of the usual FET, with
a drain, a source, a narrow channel, and a gate for con-
trolling the current. The gate either allows the current to
flow (ON) or does not (OFF). The spin transistor is simi-
1 While there are proposals for spintronic devices based on deoxyri-
bonucleic acid (DNA) molecules (Zwolak and Di Ventra, 2002),
the whole device, which includes electrodes, voltage/current
source, etc., is still a solid-state system.
Ω
k
n





















































































FIG. 1 Scheme of the Datta-Das spin field-effect transistor
(SFET). The source (spin injector) and the drain (spin detec-
tor) are ferromagnetic metals or semiconductors, with par-
allel magnetic moments. The injected spin-polarized elec-
trons with wave vector k move ballistically along a quasi-
one-dimensional channel formed by, for example, an In-
GaAs/InAlAs heterojunction in a plane normal to n. Electron
spins precess about the precession vector Ω, which arises from
spin-orbit coupling and which is defined by the structure and
the materials properties of the channel. The magnitude of Ω
is tunable by the gate voltage VG at the top of the channel.
The current is large if the electron spin at the drain points in
the initial direction (top row), for example, if the precession
period is much larger than the time of flight, and small if the
direction is reversed (bottom).
lar in that the result is also a control of the charge current
through the narrow channel. The difference, however, is
in the physical realization of the current control. In the
Datta-Das SFET the source and the drain are ferromag-
nets acting as the injector and detector of the electron
spin. The drain injects electrons with spins parallel to
the transport direction. The electrons are transported
ballistically through the channel. When they arrive at
the drain, their spin is detected. In a simplified picture,
the electron can enter he drain (ON) if its spin points
in the same direction as the spin of the drain. Other-
wise it is scattered away (OFF). The role of the gate is
to generate an effective magnetic field (in the direction
of Ω in Fig. 1), arising from the spin-orbit coupling in
the substrate material, from the confinement geometry
of the transport channel, and the electrostatic potential
of the gate. This effective magnetic field causes the elec-
tron spins to precess. By modifying the voltage, one can
cause the precession to lead to either parallel or antipar-
allel (or anything between) electron spin at the drain,
effectively controlling the current.
Even though the name spintronics is rather novel,2
contemporary research in spintronics relies closely on
a long tradition of results obtained in diverse areas of
physics (for example, magnetism, semiconductor physics,
2 The term was coined by S. A. Wolf in 1996, as a name for a
DARPA initiative for novel magnetic materials and devices.

3superconductivity, optics, and mesoscopic physics) and
establishes new connections between its different sub-
fields (Rashba, 2002d; Zˇutic´, 2002). We review here both
well-established results and the physical principles rele-
vant to the present and future applications. Our strategy
is to give a comprehensive view of what has been accom-
plished, focusing in detail on a few selected topics that we
believe are representative for the broader subject within
which they appear. For example, while discussing the
generation of spin polarization, we survey many experi-
mental and theoretical studies of both optical orientation
and electrical spin injection and present a detailed and
self-contained formalism of electrical spin injection. Sim-
ilarly, when we discuss spin relaxation, we give a catalog
of important work, while studying spin relaxation in the
cases of Al and GaAs as representative of the whole field.
Finally, in the section on spin devices we give detailed
physical principles of several selected devices, such as,
for example, the above-mentioned Datta-Das SFET.
There have been many other reviews written on spin-
tronics, most focusing on a particular aspect of the field.
We divide them here, for an easier orientation, into two
groups, those that cover the emerging applications3 and
those covering already well-established schemes and ma-
terials4 The latter group, often described as magneto-
electronics typically covers paramagnetic and ferromag-
netic metals and insulators, which utilize magnetore-
sistive effects, realized, for example, as magnetic read
heads in computer hard drives, nonvolatile magnetic
random access memory (MRAM), and circuit isolators
(Wang et al., 2002). These more established aspects of
spintronics have been also addressed in several books5
and will be discussed in another review,6 complementary
to ours.
Spintronics also benefits from a large class of emerg-
ing materials, such as ferromagnetic semiconductors
(Ohno, 1998; Pearton et al., 2003), organic semiconduc-
tors (Dediu et al., 2002), organic ferromagnets (Epstein,
2003; Pejakovic´ et al., 2002), high temperature supercon-
ductors (Goldman et al., 1999), and carbon nanotubes
(Tsukagoshi et al., 1999; Zhao et al., 2002), which can
bring novel functionalities to the traditional devices.
There is a continuing need for fundamental studies before
the potential of spintronic applications is fully realized.
3 Reviews on emerging application include those of (Das Sarma,
2001; Das Sarma et al., 2000a,b, 2001, 2000c; Oestreich et al.,
2002; Rashba, 2002d; Wolf et al., 2001; Wolf and Treger, 2000;
Zˇutic´, 2002; Zˇutic´ (Ed.), 2002).
4 Established schemes and materials are reviewed by (Ansermet,
1998; Bass and Pratt, Jr., 1999; Daughton et al., 1999;
Gijs and Bauer, 1997; Gregg et al., 1997; Prinz, 1995, 1998;
Stiles, 2004; Tedrow and Meservey, 1994).
5 See, for example, the books of (Chtchelkanova et al., 2003;
Hartman (Ed.), 2000; Hirota et al., 2002; Levy and Mertig,
2002; Maekawa et al., 2002; Parkin, 2002; Shinjo, 2002;
Ziese and Thornton (Eds.), 2001)
6 In preparation by S. S. P. Parkin for Review Modern Physics.
After an overview, Sec. I covers some basic histori-
cal and background material, part of which has already
been extensively covered in the context of magnetoelec-
tronics and will not be discussed further in this review.
Techniques for generating spin polarization, focusing on
optical spin orientation and electrical spin injection, are
described in Sec. II. The underlying mechanisms respon-
sible for the loss of spin orientation and coherence, which
impose fundamental limits on the length and time scales
in spintronic devices, are addressed in Sec. III. Spin-
tronic applications and devices, with the emphasis on
those based on semiconductors, are discussed in Sec. IV.
The review concludes with a look at future prospects in
Sec. V and with the table (Tab. II) listing the most com-
mon abbreviations used in the text.
B. History and background
1. Spin-polarized transport and magnetoresistive effects
In a pioneering work, Mott (1936a,b) provided a basis
for our understanding of spin-polarized transport. Mott
sought an explanation for an unusual behavior of resis-
tance in ferromagnetic metals. He realized that at suf-
ficiently low temperatures, where magnon scattering be-
comes vanishingly small, electrons of majority and minor-
ity spin, with magnetic moment parallel and antiparallel
to the magnetization of a ferromagnet, respectively, do
not mix in the scattering processes. The conductivity
can then be expressed as the sum of two independent
and unequal parts for two different spin projections–the
current in ferromagnets is spin polarized. This is also
known as the two-current model and has been extended
by Campbell et al. (1967); Fert and Campbell (1968). It
continues, in its modifications, to provide an explanation
for various magnetoresistive phenomena (Valet and Fert,
1993).
Tunneling measurements played a key role in early ex-
perimental work on spin-polarized transport. Studying
N/F/N junctions, where N was a nonmagnetic7 metal
and F was an Eu-based ferromagnetic semiconductor
(Kasuya and Yanase, 1968; Nagaev, 1983), revealed that
I-V curves could be modified by an applied magnetic
field (Esaki et al., 1967) and show potential for develop-
ing a solid-state spin-filter. When unpolarized current is
passed across a ferromagnetic semiconductor, the current
becomes spin-polarized (Hao et al., 1990; Moodera et al.,
1988).
A series of experiments (Tedrow and Meservey, 1971b,
1973, 1994) in ferromagnet/insulator/superconductor
7 Unless explicitly specified, we shall use the terms “nonmagnetic”
and “paramagnetic” interchangeably, i.e., assume that they both
refer to a material with no long-range ferromagnetic order and
with Zeeman-split carrier spin subbands in an applied magnetic
field.

4F2F1 F2F1
(a)
E E
I I
(b)
E E
N (E) N (E) N (E) N (E) N (E) N (E) N (E) N (E)
∆ex
subband
minority−spin majority−spin
subband
FIG. 2 Schematic illustration of electron tunneling in ferro-
magnet/insulator/ferromagnet (F/I/F) tunnel junctions: (a)
Parallel and (b) antiparallel orientation of magnetizations
with the corresponding spin-resolved density of the d states
in ferromagnetic metals that have exchange spin splitting
∆ex. Arrows in the two ferromagnetic regions are deter-
mined by the majority-spin subband. Dashed lines depict
spin-conserved tunneling.
(F/I/S) junctions has unambiguously proved that the
tunneling current remains spin-polarized even outside of
the ferromagnetic region.8 The Zeeman-split quasipar-
ticle density of states in a superconductor (Fulde, 1973;
Tedrow et al., 1970) was used as a detector of spin polar-
ization of conduction electrons in various magnetic ma-
terials. Julliere` (1975) measured tunneling conductance
of F/I/F junctions, where I was an amorphous Ge. By
adopting the Tedrow and Meservey (1971b, 1973) analy-
sis of the tunneling conductance from F/I/S to the F/I/F
junctions, Julliere` (1975) formulated a model for a change
of conductance between the parallel (↑↑) and antiparallel
(↑↓) magnetization in the two ferromagnetic regions F1
and F2, as depicted in Fig. 2. The corresponding tun-
neling magnetoresistance9 (TMR) in an F/I/F magnetic
tunnel junction (MTJ) is defined as
TMR = ∆RR↑↑
=
R↑↓ −R↑↑
R↑↑
=
G↑↑ −G↑↓
G↑↓
, (1)
where conductance G and resistance R=1/G are labeled
by the relative orientations of the magnetizations in F1
and F2 (it is possible to change the relative orientations,
between ↑↑ and ↑↓, even at small applied magnetic fields
∼ 10 G). TMR is a particular manifestation of a magne-
toresistance (MR) that yields a change of electrical resis-
8 It has been shown that electrons photoemitted from ferromag-
netic gadolinium remain spin polarized (Busch et al., 1969).
9 Starting with Julliere` (1975) an equivalent expression (G↑↑ −
G↑↓)/G↑↑ has also also used by different authors and
often referred to as junction magnetoresistance (JMR)
(Moodera and Mathon, 1999).
tance in the presence of an external magnetic field.10 His-
torically, the anisotropic MR in bulk ferromagnets such
as Fe and Ni was discovered first, dating back the to
experiments of Lord Kelvin (Thomson, 1857). Due to
spin-orbit interaction, electrical resistivity changes with
the relative direction of the charge current (for example,
parallel or perpendicular) with respect to the direction
of magnetization.
Within Jullie`re’s model, which assumes constant tun-
neling matrix elements and that electrons tunnel without
spin flip, Eq. (1) yields
TMR = 2P1P2
1− P1P2
, (2)
where the polarization Pi = (NMi −Nmi)/(NMi +Nmi)
is expressed in terms of the spin-resolved density of
states NMi and Nmi, for majority and minority spin
in Fi, respectively. Conductance in Eq. (1) can then
be expressed as (Maekawa and Ga¨fvert, 1982) G↑↑ ∼
NM1NM2+Nm1Nm2 and G↑↓ ∼ NM1Nm2+Nm1NM2 to
give Eq. (2).11 While the early results of Julliere` (1975)
were not confirmed, TMR at 4.2 K was observed using
NiO as a tunnel barrier by Maekawa and Ga¨fvert (1982).
The prediction of Jullie`re’s model illustrates the spin-
valve effect: the resistance of a device can be changed
by manipulating the relative orientation of the mag-
netizations M1 and M2, in F1 and F2, respectively.
Such orientation can be preserved even in the absence
of a power supply and the spin-valve effect,12 later
discovered in multilayer structures displaying the giant
magnetoresistance (GMR) effect,13 (Baibich et al., 1988;
Binasch et al., 1989) can be used for nonvolatile memory
applications (Hartman (Ed.), 2000; Hirota et al., 2002;
Parkin, 2002). GMR structures are often classified ac-
cording whether the current flows parallel (CIP) or per-
pendicular (CPP) to the interfaces between the different
layers, as depicted in Fig. 3. Most of the GMR applica-
tions use the CIP geometry, while the CPP version, first
realized by (Pratt, Jr. et al., 1991), is easier to analyze
theoretically (Gijs and Bauer, 1997; Levy and Mertig,
2002) and relates to the physics of the TMR effect
(Mathon and Umerski, 1997). The size of magnetore-
sistance in the GMR structures can be expressed anal-
ogously to Eq. (1), where parallel and antiparallel orien-
tations of the magnetizations in the two ferromagnetic
10 The concept of TMR was proposed independently by R. C.
Barker in 1975 [see Meservey et al. (1983)] and by Slonczewski
(1976), who envisioned its use for magnetic bubble memory
(Parkin, 2002).
11 In IV we address some limitations of the Jullie`re’s model and its
potential ambiguities to identify precisely which spin polarization
is actually measured.
12 The term was coined by Dieny et al. (1991) in the context of
GMR, by invoking an analogy with the physics of the TMR.
13 The term “giant” reflected the magnitude of the effect (more
than ∼ 10 %), as compared to the better known anisotropic
magnetoresistance (∼ 1 %).

5















































































































































































































































































































































F FN
F
F
N
(b)(a) current flowcurrent flow
FIG. 3 Schematic illustration of (a) the current in plane
(CIP) (b) the current perpendicular to the plane (CPP) giant
magnetoresistance geometry.
regions are often denoted by “P” and “AP,” respectively
(instead of ↑↑ and ↑↓). Realization of a large room tem-
perature GMR (Parkin et al., 1991a,b) enabled a quick
transition from basic physics to commercial applications
in magnetic recording (Parkin et al., 2003).
One of the keys to the success of the MR-based-
applications is their ability to control14 the relative orien-
tation of M1 and M2. An interesting realization of such
control was proposed independently by Berger (1996)
and Slonczewski (1996). While in GMR or TMR struc-
tures the relative orientation of magnetizations will af-
fect the flow of spin-polarized current, they predicted a
reverse effect. The flow of spin-polarized current can
transfer angular momentum from carriers to ferromag-
net and alter the orientation of the corresponding mag-
netization, even in the absence of an applied magnetic
field. This phenomenon, known as spin-transfer torque,
has since been extensively studied both theoretically
and experimentally (Bazaliy et al., 1998; Myers et al.,
1999; Stiles and Zangwill, 2002; Sun, 2000; Tsoi et al.,
1998; Waintal et al., 2000) and current-induced mag-
netization reversal was demonstrated at room temper-
ature (Katine et al., 2000). It was also shown that
the magnetic field generated by passing the current
through a CPP GMR device could produce room temper-
ature magnetization reversal (Bussmann et al., 1999). In
the context of ferromagnetic semiconductors additional
control of magnetization was demonstrated optically
(by shining light) (Boukari et al., 2002; Koshihara et al.,
1997; Oiwa et al., 2002) and electrically (by applying
gate voltage) (Boukari et al., 2002; Ohno et al., 2000a;
Park et al., 2002) to perform switching between the fer-
romagnetic and paramagnetic states.
Jullie`re’s model also justifies the continued quest
for highly spin-polarized materials – they would pro-
vide large magnetoresistive effects, desirable for de-
vice applications. In an extreme case, spins would
be completely polarized even in the absence of mag-
netic field. Numerical support for the existence of
such materials–the so called half-metallic ferromag-
14 For example, with small magnetic field (Parkin, 2002) or at high
switching speeds (Schumacher et al., 2003a,b).
nets15 was provided by de Groot et al. (1983b), and
these materials were reviewed by Pickett and Moodera
(2001). In addition to ferromagnets, such as CrO2
(Parker et al., 2002; Soulen Jr. et al., 1998) and man-
ganite perovskites (Park et al., 1998a), there is evi-
dence for high spin polarization in III-V ferromagnetic
semiconductors like (Ga,Mn)As (Braden et al., 2003;
Panguluri et al., 2003a). The challenge remains to pre-
serve such spin polarization above room temperature and
in junctions with other materials, since the surface (inter-
face) and bulk magnetic properties can be significantly
different (Falicov et al., 1990; Fisher, 1967; Mills, 1971).
While many existing spintronic applications
(Hartman (Ed.), 2000; Hirota et al., 2002) are based
on the GMR effects, the discovery of large room-
temperature TMR (Miyazaki and Tezuka, 1995;
Moodera et al., 1995) has renewed interest in the
study of magnetic tunnel junctions which are now the
basis for the several MRAM prototypes16 (Parkin et al.,
1999; Tehrani et al., 2000). Future generations of
magnetic read heads are expected to use MTJ’s instead
of CIP GMR. To improve the switching performance of
related devices it is important to reduce the junction
resistance, which determines the RC time constant of
the MTJ cell. Consequently, semiconductors, which
would provide a lower tunneling barrier than the usually
employed oxides, are being investigated both as the
non-ferromagnetic region in MTJ’s and as the basis
for an all-semiconductor junction that would demon-
strate large TMR at low temperatures (Tanaka, 2002;
Tanaka and Higo, 2001). Another desirable property of
semiconductors has been demonstrated by the extraor-
dinary large room-temperature MR in hybrid structures
with metals reaching 750 000% at a magnetic field of
4 T (Solin et al., 2000) which could lead to improved
magnetic read heads (Moussa et al., 2003; Solin et al.,
2002). MR effects of similar magnitude have also
been found in hybrid metal/semiconductor granular
films (Akinaga, 2002). Another approach to obtaining
large room-temperature magnetoresistance (> 100%
at B ∼ 100 G) is to fabricate ferromagnetic regions
separated by a nanosize contact. For simplicity, such
a structure could be thought of as the limiting case of
the CPP GMR scheme in Fig. 3(b). This behavior, also
known as ballistic magnetoresistance, has already been
studied in a large number of materials and geometries
(Bruno, 1999; Chung et al., 2002; Garcia et al., 1999;
Imamura et al., 2000; Tatara et al., 1999; Versluijs et al.,
2001).
15 Near the Fermi level they behave as metals only for one spin, the
density of states vanishes completely for the other spin.
16 Realization of the early MRAM proposals used the effect of
anisotropic magnetoresistance (Pohm et al., 1987, 1988).

62. Spin injection and optical orientation
Many materials in their ferromagnetic state can have
a substantial degree of equilibrium carrier spin polariza-
tion. However, as illustrated in Fig. 1, this alone is
usually not sufficient for spintronic applications, which
typically require current flow and/or manipulation of
the nonequilibrium spin (polarization).17 The impor-
tance of generating nonequilibrium spin is not limited
to device applications; it can also be used as a sensitive
spectroscopic tool to study a wide variety of fundamen-
tal properties ranging from spin-orbit and hyperfine in-
teractions (Meier and Zakharchenya (Eds.), 1984) to the
pairing symmetry of high temperature superconductors
(Ngai et al., 2004; Tsuei and Kirtley, 2000; Vas’ko et al.,
1997; Wei et al., 1999) and the creation of spin-polarized
beams to measure parity violation in high energy physics
(Pierce and Celotta, 1984).
Nonequilibrium spin is the result of some source of
pumping arising from transport, optical, or resonance
methods. Once the pumping is turned off the spin will
return to its equilibrium value. While for most applica-
tions it is desirable to have long spin relaxation times,
it has been demonstrated that short spin relaxation
times are useful in the implementation of fast switching
(Nishikawa et al., 1995).
Electrical spin injection, an example of a transport
method for generating nonequilibrium spin, has already
been realized experimentally by Clark and Feher (1963),
who drove a direct current through a sample of InSb in
the presence of constant applied magnetic filed. The prin-
ciple was based on the Feher effect,18 in which the hy-
perfine coupling between the electron and nuclear spins,
together with different temperatures representing elec-
tron velocity and electron spin populations, is responsible
for the dynamical nuclear polarization (Slichter, 1989).19
17 Important exceptions are tunneling devices operating at low bias
and near equilibrium spin. Equilibrium polarization and the cur-
rent flow can be potentially realized, for example, in spin-triplet
superconductors and thin-film ferromagnets (Ko¨nig et al., 2001),
accompanied by dissipationless spin currents. Using an analogy
with the quantum Hall effect, it has been suggested that the
spin-orbit interaction could lead to dissipationless spin currents
in hole-doped semiconductors (Murakami et al., 2003). Rashba
(2003b) has pointed out that similar dissipationless spin currents
in thermodynamic equilibrium, due to spin-orbit interaction, are
not transport currents which could be employed for transporting
spins and spin injection. It is also instructive to compare several
earlier proposals that use spin-orbit coupling to generate spin
currents, discussed in Sec. II.A.
18 The importance and possible applications of the Feher ef-
fect (Feher, 1959) to polarize electrons was discussed by
(Das Sarma et al., 2000b; Suhl, 2002).
19 Such an effect can be thought of as a generalization of the Over-
hauser effect (Overhauser, 1953b) in which the use of a resonant
microwave excitation causes the spin relaxation of the nonequi-
librium electron population through hyperfine coupling to lead
to the spin polarization of nuclei. Feher (1959) suggested several
other methods, instead of microwave excitation, that could pro-
δM
δM
µ0
NF
x0
(a)
E E
(c)
(b) M
N (E) N (E) N (E) N (E)
j
FIG. 4 Pedagogical illustration of the concept of electrical
spin injection from a ferromagnet (F) into a normal metal (N).
Electrons flow from F to N: (a) schematic device geometry;
(b) magnetization M as a function of position. Nonequilib-
rium magnetization δM (spin accumulation) is injected into
a normal metal; (c) contribution of different spin-resolved
densities of states to charge and spin transport across the
F/N interface. Unequal filled levels in the density of states
depict spin-resolved electrochemical potentials different from
the equilibrium value µ0.
Motivated by the work of Clark and Feher (1963),
Tedrow and Meservey (1971b, 1973), and the principle
of optical orientation (Meier and Zakharchenya (Eds.),
1984), Aronov (1976a,b) and Aronov and Pikus (1976)
established several key concepts in electrical spin injec-
tion from ferromagnets into metals, semiconductors20
and superconductors. When a charge current flowed
across the F/N junction (Fig. 4) Aronov (1976b) pre-
dicted that spin-polarized carriers in a ferromagnet would
contribute to the net current of magnetization entering
the nonmagnetic region and would lead to nonequilib-
rium magnetization δM , depicted in Fig. 4(b), with the
spatial extent given by the spin diffusion length (Aronov,
1976b; Aronov and Pikus, 1976).21 Such δM , which is
also equivalent to a nonequilibrium spin accumulation,
was first measured in metals by Johnson and Silsbee
(1985, 1988d). In the steady state δM is realized as
the balance between spins added by the magnetization
current and spins removed by spin relaxation.22
duce a nonequilibrium electron population and yield a dynamical
polarization of nuclei [see also Weger (1963)].
20 In an earlier work spin injection of minority carriers was pro-
posed in a ferromagnet/insulator/p-type semiconductor struc-
ture. Measuring polarization of electroluminescence was sug-
gested as a technique for detecting injection of polarized carriers
in a semiconductor (Scifres et al., 1973).
21 Supporting the findings of Clark and Feher (1963), Aronov cal-
culated that the electrical spin injection would polarize nuclei
and lead to a measurable effect in the electron spin resonance
(ESR). Several decades later related experiments on spin injec-
tion are also examining other implications of dynamical nuclear
polarization (Johnson, 2000; Strand et al., 2003).
22 The spin diffusion length is an important quantity for CPP GMR.
The thickness of the N region in Fig. 3 should not exceed the spin
diffusion length, otherwise the information on the orientation of

7Generation of nonequilibrium spin polarization and
spin accumulation is also possible by optical methods
known as optical orientation or optical pumping. In
optical orientation, the angular momentum of absorbed
circularly polarized light is transferred to the medium.
Electron orbital momenta are directly oriented by light
and through spin-orbit interaction electron spins be-
come polarized. In II.B we focus on the optical ori-
entation in semiconductors, a well-established technique
(Meier and Zakharchenya (Eds.), 1984). In a pioneer-
ing work Lampel (1968) demonstrated that spins in sil-
icon can be optically oriented (polarized). This tech-
nique is derived from optical pumping proposed by
Kastler (1950) in which optical irradiation changes the
relative populations within the Zeeman and the hy-
perfine levels of the ground states of atoms. While
there are similarities with previous studies of free atoms
(Cohen-Tannoudji and Kostler, 1966; Happer, 1972), op-
tical orientation in semiconductors has important differ-
ences related to the strong coupling between the electron
and nuclear spin and macroscopic number of particles
(Hermann et al., 1985; Meier and Zakharchenya (Eds.),
1984; Paget et al., 1977). Polarized nuclei can exert large
magnetic fields (∼ 5 T) on electrons. In bulk III-V semi-
conductors, such as GaAs, optical orientation can lead
to 50% polarization of electron density which could be
further enhanced in quantum structures of reduced di-
mensionality or by applying a strain. A simple reversal
in the polarization of the illuminating light (from posi-
tive to negative helicity) also reverses the sign of the elec-
tron density polarization. Combining these properties of
optical orientation with the semiconductors tailored to
have a negative electron affinity allows photoemission of
spin-polarized electrons to be used as a powerful detec-
tion technique in high-energy physics and for investigat-
ing surface magnetism (Pierce and Celotta, 1984).
II. GENERATION OF SPIN POLARIZATION
A. Introduction
Transport, optical, and resonance methods (as well as
their combination) have all been used to create nonequi-
librium spin. After introducing the concept of spin po-
larization in solid-state systems we give a pedagogical
picture of electrical spin injection and detection of polar-
ized carriers. While electrical spin injection and optical
orientation will be discussed in more detail later in this
section, we also survey here several other techniques for
polarizing carriers.
Spin polarization not only of electrons, but also of
holes, nuclei, and excitations can be defined as
PX = Xs/X, (3)
the magnetization in F1 will not be transferred to the F2 region.
the ratio of the difference Xs = Xλ −X−λ and the sum
X = Xλ + X−λ, of the spin-resolved λ components for
a particular quantity X . To avoid ambiguity as to what
precisely is meant by spin polarization both the choice
of the spin-resolved components and the relevant physi-
cal quantity X need to be specified. Conventionally, λ is
taken to be ↑ or + (numerical value +1) for spin up, ↓ or
− (numerical value -1) for spin down, with respect to the
chosen axis of quantization.23 In ferromagnetic metals
it is customary to refer to ↑ (↓) as carriers with mag-
netic moment parallel (antiparallel) to the magnetiza-
tion or, equivalently, as carriers with majority (minority)
spin (Tedrow and Meservey, 1973). In semiconductors
the terms majority and minority usually refer to relative
populations of the carriers while ↑ or + and ↓ or − cor-
respond to the quantum numbers mj with respect to the
z-axis taken along the direction of the light propagation
or along the applied magnetic field (Jonker et al., 2003b;
Meier and Zakharchenya (Eds.), 1984). It is important
to emphasize that both the magnitude and the sign of
the spin polarization in Eq. (3) depends of the choice of
X , relevant to the detection technique employed, say op-
tical vs. transport and bulk vs. surface measurements
(Jonker et al., 2003b; Mazin, 1999). Even in the same
homogeneous material the measured PX can vary for
different X , and it is crucial to identify which physical
quantity—charge current, carrier density, conductivity,
or the density of states—is being measured experimen-
tally.
The spin polarization of electrical current or carrier
density, generated in a nonmagnetic region, is typically
used to describe the efficiency of electrical spin injec-
tion. Silsbee (1980) suggested that the nonequilibrium
density polarization in the N region, or equivalently the
nonequilibrium magnetization, acts as the source of spin
electromotive force (EMF) and produces a measurable
“spin-coupled” voltage Vs ∝ δM . Using this concept,
also referred to as spin-charge coupling, Silsbee (1980)
proposed a detection technique consisting of two ferro-
magnets F1 and F2 (see Fig. 5) separated by a non-
magnetic region.24 F1 serves as the spin injector (spin
aligner) and F2 as the spin detector. This could be called
the polarizer-analyzer method, the optical counterpart
of the transmission of light through two optical linear
polarizers. From Fig. 5 it follows that the reversal of
the magnetization direction in one of the ferromagnets
would lead either to Vs → −Vs, in an open circuit (in
the limit of large impedance Z), or to the reversal of
charge current j → −j, in a short circuit (at small Z),
a consequence of Silsbee-Johnson spin-charge coupling
23 For example, along the spin angular momentum, applied mag-
netic field, magnetization, or direction of light propagation.
24 A similar geometry was also proposed independently by
de Groot et al. (1983a), where F1 and F2 were two half-metallic
ferromagnets with the goal of implementing spin-based devices
to amplify and/or switch current.

8µ0
µ0










































j
Vs
E E
(b)
E
F1 F2
E
(a)
δM
(c)
E
N
F1 F2 (Z= )FN 2 (Z=0)
∆2
N (E) N (E)
Z
d
FIG. 5 Spin injection, spin accumulation, and spin detection:
(a) two idealized completely polarized ferromagnets F1 and
F2 (the spin down density of states N↓ is zero at the energy
of electrochemical potential E = µ0) with parallel magnetiza-
tions are separated by the nonmagnetic region N; (b) density-
of-states diagrams for spin injection from F1 into N, accompa-
nied by the spin accumulation–generation of the nonequilib-
rium magnetization δM . At F2 in the limit of low impedance
(Z=0) spin is detected by measuring the spin-polarized cur-
rent across the N/F2 interface. In the limit of high impedance
(Z = ∞) spin is detected by measuring the voltage Vs ∼ δM
developed across the N/F2 interface; (c) spin accumulation in
a device in which a superconductor (with the superconducting
gap ∆) is occupying the region between F1 and F2.
(Johnson and Silsbee, 1987, 1988a; Silsbee, 1980). Cor-
respondingly, as discussed in the following sections, the
spin injection could be detected through the spin accumu-
lation signal either as a voltage or the resistance change
when the magnetizations in F1 and F2 are changed from
parallel to antiparallel alignment.
Since the experiments demonstrating the spin
accumulation of conduction electrons in metals
(Johnson and Silsbee, 1985), spin injection has been
realized in a wide range of materials. While in Sec. II.C
we focus on related theoretical work motivated by po-
tential applications, experiments on spin injection have
also stimulated proposals for examining the fundamental
properties of electronic systems.25
The generation of nonequilibrium spin polarization
has a long tradition in magnetic resonance methods
(Abragam, 1961; Slichter, 1989). However, transport
methods to generate carrier spin polarization are not lim-
ited to electrical spin injection. For example, they also
25 For example, studies probing the spin-charge separation in the
non-Fermi liquids have been proposed by (Balents and Egger,
2000, 2001; Kivelson and Rokhsar, 1990; Si, 1997, 1998;
Zhao and Hershfield, 1995). Spin and charge are carried by sep-
arate excitations and can lead to spatially separated spin and
charge currents (Kivelson and Rokhsar, 1990).
include scattering of unpolarized electrons in the presence
of spin-orbit coupling (Kessler, 1976; Mott and Massey,
1965) and in materials that lack the inversion symmetry
(Levitov et al., 1984), adiabatic (Mucciolo et al., 2002;
Sharma and Chamon, 2003; Watson et al., 2003) and
nonadiabatic quantum spin pumping (Zheng et al., 2003)
[for an instructive description of parametric pumping see
(Brouwer, 1998)], and the proximity effects (Ciuti et al.,
2002a).
It would be interesting to know what the limits are
on the magnitude of various spin polarizations. Could
we have a completely polarized current [Pj → ∞, see
Eq. (3)], with only a spin current (j↑− j↓) and no charge
current (j↑ + j↓ = 0)? While it is tempting to recall
the Stern-Gerlach experiment and try to set up magnetic
drift through inhomogeneous magnets (Kessler, 1976),
this would most likely work only as a transient effect
(Fabian and Das Sarma, 2002). It was proposed already
by D’yakonov and Perel’ (1971a,c) that a transverse spin
current (and transverse spin polarization in a closed sam-
ple) would form as a result of spin-orbit coupling-induced
skew scattering in the presence of a longitudinal electric
field. This interesting effect, also called the spin Hall
effect (Hirsch, 1999; Zhang, 2000), has yet to be demon-
strated. An alternative scheme for producing pure spin
currents was proposed by Bhat and Sipe (2000), moti-
vated by the experimental demonstration of phase co-
herent control of charge currents (Atanasov et al., 1996;
Hache´ et al., 1997) and carrier population (Fraser et al.,
1999). A quantum-mechanical interference between one-
and two-photon absorptions of orthogonal linear polar-
izations creates an opposite ballistic flow of spin up and
spin down electrons in a semiconductor. Only a spin cur-
rent can flow, without a charge current, as demonstrated
by Stevens et al. (2003) and Hu¨bner et al. (2003), who
were able to achieve coherent control of the spin current
direction and magnitude by the polarization and the rel-
ative phase of two exciting laser light fields.
Charge current also can be driven by circularly polar-
ized light (Ivchenko and Pikus, 1997). Using the prin-
ciples of optical orientation (see Sec. I.B.2 and further
discussion in Sec. II.B) in semiconductors of reduced di-
mensionality or lower symmetry, both the direction and
the magnitude of a generated charge current can be con-
trolled by circular polarization of the light. This is called
the circular photo-voltaic effect (Ganichev and Prettl,
2003), which can be viewed as a transfer of the angular
momentum of photons to directed motion of electrons.
This could also be called a spin corkscrew effect, since a
nice mechanical analog is a corkscrew whose rotation gen-
erates linear directed motion. A related effect, in which
the photocurrent is driven, is called the spin-galvanic ef-
fect (Ganichev and Prettl, 2003). The current here is
causes by the difference in spin-flip scattering rates for
electrons with different spin states in some systems with
broken inversion symmetry. A comprehensive survey of
the related effects from the circular photo-galvanic effect
(Asnin et al., 1979) to recent demonstrations in semicon-

9σ+σ+
mj
Eg
∆
CB
SO
E
LH
HH
0 k
(a)
3/2P
1/2P
1/2S (b)
HH,LH
σ− −σ
1/2−1/2
−1/2 1/2
−3/2 3/2
−1/2 1/2
SO
CB
3 1 1 3
22
Γ7
Γ8
6Γ
so
FIG. 6 (a) Interband transitions in GaAs: (a) schematic band
structure of GaAs near the center of the Brillouin zone (Γ
point), where Eg is the band gap and ∆so is the spin-orbit
splitting; CB, conduction band; HH, valence heavy hole; LH,
light hole; SO, spin-orbit-split-off subbands; Γ6,7,8 are the
corresponding symmetries at the k = 0 point, more precisely,
the irreducible representations of the tetrahedron group Td
(Ivchenko and Pikus, 1997); (b) selection rules for interband
transitions between mj sublevels for circularly polarized light
σ+ and σ− (positive and negative helicity). The circled num-
bers denote the relative transition intensities that apply for
both excitations (depicted by the arrows) and radiative re-
combinations.
ductor quantum wells (Ganichev et al., 2002a,b, 2001,
2003)] is given by Ganichev and Prettl (2003).
There is a wide range of recent theoretical proposals for
devices that would give rise to a spin electromotive force
(Brataas et al., 2002; Governale et al., 2003; Long et al.,
2003; Mal’shukov et al., 2003; Ting and Cartoixa`, 2003;
Zˇutic´ et al., 2001a,b), often referred to as spin(-
polarized) pumps, cells, or batteries. However, even
when it is feasible to generate pure spin current, this does
not directly imply that it would be dissipationless. In the
context of superconductors, it has been shown that Joule
heating can arise from pure spin current flowing through
a Josephson junction (Takahashi et al., 2001).
B. Optical spin orientation
In a semiconductor the photoexcited spin-polarized
electrons and holes exist for the time τ before they re-
combine. If a fraction of the carriers’ initial orienta-
tion survives longer than the recombination time, that
is, if τ < τs, 26 where τs is the spin relaxation time
(see Sec. III), the luminescence (recombination radia-
tion) will be partially polarized. By measuring the cir-
cular polarization of the luminescence it is possible to
study the spin dynamics of the nonequilibrium carriers
in semiconductors (Oestreich et al., 2002) and to extract
26 In Si this condition is not fulfilled. Instead of measuring the lu-
minescence polarization, Lampel (1968) has used NMR to detect
optical spin orientation.
Symmetry |J,mj〉 Wave function
Γ6 |1/2, 1/2〉 |S ↑〉
|1/2,−1/2〉 |S ↓〉
Γ7 |1/2, 1/2〉 | − (1/3)1/2[ (X + iY )↓ −Z ↑] 〉
|1/2,−1/2〉 |(1/3)1/2[ (X − iY )↑ +Z ↓] 〉
Γ8 |3/2, 3/2〉 |(1/2)1/2(X + iY )↑〉
|3/2, 1/2〉 |(1/6)1/2[ (X + iY )↓ +2Z ↑] 〉
|3/2,−1/2〉 | − (1/6)1/2[ (X − iY )↑ −2Z ↓] 〉
|3/2,−3/2〉 |(1/2)1/2(X − iY )↓〉
TABLE I Angular and spin part of the wave function at Γ.
such useful quantities as the spin orientation, the recom-
bination time, or the spin relaxation time of the car-
riers (Ekimov and Safarov, 1970; Garbuzov et al., 1971;
Meier and Zakharchenya (Eds.), 1984; Parsons, 1969).
We illustrate the basic principles of optical orienta-
tion by the example of GaAs which is representative of
a large class of III-V and II-VI zincblende semiconduc-
tors. The band structure is depicted in Fig. 6(a). The
band gap is Eg = 1.52 eV at T = 0 K, while the spin
split-off band is separated from the light and heavy hole
bands by ∆so = 0.34 eV. We denote the Bloch states
according to the total angular momentum J and its pro-
jection onto the positive z axis mj : |J,mj〉. Expressing
the wave functions with the symmetry of s, px, py, and
pz orbitals as |S〉, |X〉, |Y 〉, and |Z〉, respectively, the
band wave functions can be written as listed in Table I
(Pierce and Meier, 1976) [with minor typos removed, see
also (Kittel, 1963)].
To obtain the excitation (or recombination) probabil-
ities consider photons arriving in the z direction. Let
σ± represent the helicity of the exciting light. When we
represent the dipole operator corresponding to the σ±
optical transitions as 27 ∝ (X ± iY ) ∝ Y ±11 , where Y ml
is the spherical harmonic, it follows from Table I that
|〈1/2,−1/2|Y 11 |3/2,−3/2〉|2
|〈1/2, 1/2|Y 11 |3/2,−1/2〉|2
= 3 (4)
for the relative intensity of the σ+ transition between
the heavy (|mj = 3/2|) and the light (|mj = 1/2|) hole
subbands and the conduction band. Other transitions are
analogous. The relative transition rates are indicated in
Fig. 6(b). The same selection rules apply to the optical
orientation of shallow impurities (Ekimov and Safarov,
1970; Parsons, 1969).
The spin polarization of the excited electrons28. de-
pends on the photon energy h¯ω. For h¯ω between Eg
27 For an outgoing light in the −z direction the helicities are re-
versed.
28 Although holes are initially polarized too, they lose spin orien-

10
and Eg + ∆so, only the light and heavy hole subbands
contribute. Denoting by n+ and n− the density of elec-
trons polarized parallel (mj = 1/2) and antiparallel
(mj = −1/2) to the direction of light propagation, we
define the spin polarization as (see Sec. II.A)
Pn = (n+ − n−)/(n+ + n−). (5)
For our example of the zincblende structure,
Pn = (1− 3)/(3 + 1) = −1/2 (6)
is the spin polarization at the moment of photoexcita-
tion. The spin is oriented against the direction of light
propagation, since there are more transitions from the
heavy hole than from the light hole subbands. The cir-
cular polarization of the luminescence is defined as
Pcirc = (I+ − I−)/(I+ + I−), (7)
where I± is the radiation intensity for the helicity σ±.
The polarization of the σ+ photoluminescence is then
Pcirc =
(n+ + 3n−)− (3n+ + n−)
(n+ + 3n−) + (3n+ + n−)
= −Pn
2
=
1
4
. (8)
If the excitation involves transitions from the spin
split-off band, that is, if h¯ω ≫ Eg + ∆so, the elec-
trons will not be spin polarized (Pn = Pcirc = 0), un-
derlining the vital role of spin-orbit coupling for spin
orientation. On the other hand, Fig. 6 suggests that
a removal of the heavy/light hole degeneracy can sub-
stantially increase Pn (D’yakonov and Perel’, 1984a), up
to the limit of complete spin polarization. An increase
in Pn and Pcirc in GaAs strained due to a lattice mis-
match with a substrate, or due to confinement in quan-
tum well heterostructures, has indeed been demonstrated
(Oskotskij et al., 1997; Vasilev et al., 1993), detecting Pn
greater than 0.9.
While photoexcitation with circularly polarized light
creates spin-polarized electrons, the nonequilibrium
spin decays due to both carrier recombination and
spin relaxation. The steady-state degree of spin
polarization depends on the balance between the
spin excitation and decay. Sometimes a distinc-
tion is made (Meier and Zakharchenya (Eds.), 1984;
Pierce and Meier, 1976) between the terms optical spin
orientation and optical spin pumping. The former term
is used in relation to the minority carriers (such as elec-
trons in p-doped samples) and represents the orientation
of the excited carriers. The latter term is reserved for the
majority carriers (electrons in n-doped samples), repre-
senting spin polarization of the “ground” state. Both
tation very fast, on the time scale of the momentum relaxation
time (see Sec. III.D.1) However, it was suggested that manipu-
lating hole spin by short electric field pulses, between momentum
scattering events, could be useful for ultrafast spintronics appli-
cations (Dargys, 2002).
spin orientation and spin pumping were demonstrated in
the early investigations on p-GaSb (Parsons, 1969) and
p- and n-Ga0.7Al0.3As (Ekimov and Safarov, 1970, 1971;
Zakharchenya et al., 1971). Unless specified otherwise,
we shall use the term optical orientation to describe both
spin orientation and spin pumping.
To derive the steady-state expressions for the spin po-
larization due to optical orientation, consider the simple
model of carrier recombination and spin relaxation (see
Sec. IV.A.4) in a homogeneously doped semiconductor.
The balance between direct electron-hole recombination
and optical pair creation can be written as
r(np− n0p0) = G, (9)
where r measures the recombination rate, the electron
and hole densities are n and p, with index zero denoting
the equilibrium values, and G is the electron-hole pho-
toexcitation rate. Similarly, the balance between spin
relaxation and spin generation is expressed by
rsp+ s/τs = Pn(t = 0)G, (10)
where s = n+ − n− is the electron spin density and
Pn(t = 0) is the spin polarization at the moment of pho-
toexcitation, given by Eq. (5). Holes are assumed to lose
their spin orientation very fast, so they are treated as
unpolarized. The first term in Eq. (10) describes the
disappearance of the spin density due to carrier recom-
bination, while the second term describes the intrinsic
spin relaxation. From Eqs. (9) and (10) we obtain the
steady-state electron polarization as (Zˇutic´ et al., 2001b)
Pn = Pn(t = 0)
1− n0p0/np
1 + 1/τsrp
. (11)
In a p-doped sample p ≈ p0, n ≫ n0, and Eq. (11)
gives
Pn = Pn(t = 0)/(1 + τ/τs), (12)
where τ = 1/rp0 is the electron lifetime.29 The steady-
state polarization is independent of the illumination in-
tensity, being reduced from the initial spin polarization
Pn(t = 0). 30 The polarization of the photoluminescence
is Pcirc = Pn(t = 0)Pn (Parsons, 1969). Early measure-
ments of Pn = 0.42 ± 0.08 in GaSb (Parsons, 1969) and
Pn = 0.46 ± 0.06 in Ga0.7Al0.3As (Ekimov and Safarov,
1970) showed an effective spin orientation close to the
29 After the illumination is switched off, the electron spin density,
or equivalently the nonequilibrium magnetization, will decrease
exponentially with the inverse time constant 1/Ts = 1/τ + 1/τs
(Parsons, 1969).
30 The effect of a finite length for the light absorption on Pn is
discussed by Pierce and Celotta (1984). The absorption length
α−1 is typically a micron for GaAs. It varies with frequency
roughly as α(h¯ω) ∝ (h¯ω − Eg)1/2 (Pankove, 1971).

11
maximum value of Pn(t = 0) = 1/2 for a bulk unstrained
zincblende structure, indicating that τ/τs ≪ 1.
For spin pumping in an n-doped sample, where
n ≈ n0 and p ≫ p0, Eqs. (9) and (11) give
(D’yakonov and Perel’, 1971b)
Pn = Pn(t = 0)/(1 + n0/Gτs). (13)
In contrast to the previous case, the carrier (now hole)
lifetime τ = 1/rn0 has no effect on Pn. However, Pn
depends on the photoexcitation intensity G, as expected
for a pumping process. The effective carrier lifetime is
τJ = n0/G, where J represents the intensity of the il-
luminating light. If it is comparable to or shorter than
τs, spin pumping is very effective. Spin pumping works
because the photoexcited spin-polarized electrons do not
need to recombine with holes. There are plenty of un-
polarized electrons in the conduction band available for
recombination. The spin is thus pumped in to the elec-
tron system.
When magnetic field B is applied perpendicular to the
axis of spin orientation (transverse magnetic field), it
will induce spin precession with the Larmor frequency
ΩL = µBgB/h¯, where µB is the Bohr magneton and g
is the electron g factor.31 The spin precession, together
with the random character of carrier generation or dif-
fusion, leads to the spin dephasing (see Sec. III.A.1).
Consider spins excited by circularly polarized light (or
by any means of spin injection) at a steady rate. In a
steady rate a balance between nonequilibrium spin gen-
erated and spin relaxation is maintained, resulting in a
net magnetization. If a transverse magnetic field is ap-
plied, the decrease of the steady-state magnetization can
have two sources: (a) spins which were excited at ran-
dom time and (b) random diffusion of spins towards a
detection region. Consequently, spins precess along the
applied field acquiring random phases relative to those
which were excited or have arrived at different times. As
a result, the projection of the electron spin along the ex-
citing beam will decrease with the increase of transverse
magnetic field, leading to depolarization of the lumines-
cence. This is also known as the Hanle effect (Hanle,
1924), in analogy to the depolarization of the resonance
fluorescence of gases. The Hanle effect was first measured
in semiconductors by Parsons (1969). The steady-state
spin polarization of the precessing electron spin can be
calculated by solving the Bloch-Torrey equations (Bloch,
1946; Torrey, 1956), Eqs. (52)–(54) describing the spin
dynamics of diffusing carriers.
In p-doped semiconductors the Hanle curve shows a
Lorentzian decrease of the polarization (Parsons, 1969),
Pn(B) = Pn(B = 0)/(1 + ΩLTs)2, where Pn(B = 0)
is the polarization at B = 0 from Eq. (12) and T−1s is
the effective spin lifetime given by 1/Ts = 1/τ + 1/τs;
31 In our convention the g factor of free electrons is positive, g0 =
2.0023 (Kittel, 1996).
see footnote 26. Measurements of the Hanle curve in
GaAlAs were used by Garbuzov et al. (1971) to sep-
arately determine both τ and τs at various tempera-
tures. The theory of the Hanle effect in n-doped semicon-
ductors was developed by D’yakonov and Perel’ (1976)
who showed the non-Lorentzian decay of the lumines-
cence for the regimes both of low (τJ/τs ≫ 1) and
high (τJ/τs ≪ 1) intensity of the exciting light. At
high fields Pn(B) ∝ 1/B1/2, consistent with the exper-
iments of Vekua et al. (1976) in Ga0.8Al0.2As, showing
a Hanle curve different from the usual Pn(B) ∝ 1/B2
Lorentzian behavior (D’yakonov and Perel’, 1984a). Re-
cent findings on the Hanle effect in nonuniformly doped
GaAs and reanalysis of some earlier studies are given by
Dzihoev et al. (2003).
C. Theories of spin injection
Reviews on spin injection have covered materials rang-
ing from semiconductors to high temperature supercon-
ductors and have addressed the implications for device
operation as well as for fundamental studies in solid state
systems.32. In addition to degenerate conductors, exam-
ined in these works, we also give results for nondegener-
ate semiconductors in which the violation of local charge
neutrality, electric fields, and carrier band bending re-
quire solving the Poisson equation. The notation intro-
duced here emphasizes the importance of different (and
inequivalent) spin polarizations arising in spin injection.
1. F/N junction
A theory of spin injection across a ferromagnet/normal
metal (F/N) interface was first offered by Aronov
(1976b). Early work also included spin injection
into a semiconductor (Sm) (Aronov and Pikus, 1976;
Masterov and Makovskii, 1979) and a superconductor
(S) (Aronov, 1976a). Spin injection in F/N junctions was
subsequently studied in detail by Johnson and Silsbee
(1987, 1988a),33 van Son et al. (1987), Valet and Fert
(1993), Hershfield and Zhao (1997), and others. Here we
follow the approach of Rashba (2000, 2002c) and consider
a steady-state34 flow of electrons along the x direction in
32 See, for example, (Goldman et al., 2001, 1999; Jedema et al.,
2002d; Johnson, 2001, 2002a; Maekawa et al., 2001; Osofsky,
2000; Schmidt and Molenkamp, 2002; Tang et al., 2002; Wei,
2002)
33 Johnson and Silsbee base their approach on irreversible thermo-
dynamics and consider also the effects of a temperature gradient
on spin-polarized transport, omitted in this section.
34 Even some dc spin injection experiments are actually performed
at low (audio-frequency) bias. Generalization to ac spin injec-
tion, with a harmonic time dependence, was studied by Rashba
(2002b).

13
σ↑D↓)/σ = N (N↓/D↑ +N↑/D↓)−1. Using Eq. (15) and
the local charge quasineutrality δn↑ + δn↓ = 0 shows
that µs is proportional to the nonequilibrium spin den-
sity δs = δn↑ − δn↓ (s = s0 + δs = n↑ − n↓)
µs =
1
2q
N↑ +N↓
N↑N↓
δs. (22)
Correspondingly, µs is often referred to as the (nonequi-
librium) spin accumulation39 and is used to explain the
GMR effect in CPP structures (Gijs and Bauer, 1997;
Hartman (Ed.), 2000; Hirota et al., 2002; Johnson, 1991;
Valet and Fert, 1993).
The preceding equations are simplified for the N region
by noting that σλ = σ/2, σs = 0, and Dλ = D. Quanti-
ties pertaining to a particular region are denoted by the
index F or N.
Equation (21) has also been used to study the diffu-
sive spin-polarized transport and spin accumulation in
ferromagnet/superconductor structures (Jedema et al.,
1999). Some care is needed to establish the appropri-
ate boundary conditions at the F/N interface. In the
absence of spin-flip scattering40 at the F/N interface
(which can arise, for example, due to spin-orbit cou-
pling or magnetic impurities) the spin current is con-
tinuous and thus PjF (0−) = PjN (0+) ≡ Pj (omitting
x = 0± for brevity, and superscripts ± in other quanti-
ties). These boundary conditions were used by Aronov
(1976b); Aronov and Pikus (1976) without relating Pj to
the effect of the F/N contact or material parameters in
the F region.
Unless the F/N contact is highly transparent, µλ is
discontinuous across the interface (Hershfield and Zhao,
1997; Johnson and Silsbee, 1988c; Rashba, 2000;
Valet and Fert, 1993) and the boundary condition is
jλ(0) = Σλ[µλN (0)− µλF (0)], (23)
where
Σ = Σ↑ +Σ↓ (24)
is the contact conductivity. For a free-electron model
Σ↑ 6= Σ↓ can be simply inferred from the effect of the ex-
change energy, which would yield spin-dependent Fermi
wave vectors and transmission coefficients. A microscopic
determination of the corresponding contact resistance
[see Eq. (27)] is complicated by the influence of disor-
der, surface roughness, and different scattering mecha-
nisms and is usually obtained from model calculations
39 Spin accumulation is also relevant to a number of physical phe-
nomena outside the scope of this article, for example, to the
tunneling rates in the quantum Hall regime (Chan et al., 1999;
MacDonald, 1999).
40 The effects of non-conserving interfacial scattering on spin in-
jection were considered in (Fert and Lee, 1996; Rashba, 2002c;
Valet and Fert, 1993).
(Schep et al., 1997; Stiles and Penn, 2000). Continued
work on the first-principles calculation of F/N interfaces
(Erwin et al., 2002; Stiles, 1996) is needed for a more de-
tailed understanding of spin injection. From Eqs. (23)
and (24) it follows that
µsN (0)− µsF (0) = 2rc(Pj − PΣ)j, (25)
µN (0)− µF (0) = rc(1 − PΣPj)j, (26)
where the effective contact resistance is
rc = Σ/4Σ↑Σ↓. (27)
The decay of µs, away from the interface, is characterized
by the corresponding spin diffusion length
µsF = µsF (0)ex/LsF , µsN = µsN (0)e−x/LsN . (28)
A nonzero value for µsN (0) implies the existence of
nonequilibrium magnetization δM in the N region (for
noninteracting electrons qµs = µBδM/χ, where χ
is the magnetic susceptibility). Such a δM , as a
result of electrical spin injection, was proposed by
Aronov and Pikus (1976) and first measured in metals
by Johnson and Silsbee (1985).
By applying Eq. (19), separately, to the F and N re-
gions, one can obtain the amplitude of spin accumulation
in terms of the current and density of states spin polar-
ization and the effective resistances rF and rN ,
µsF (0) = 2rF [Pj − PσF ] j, µsN (0) = −2rNPjj, (29)
where
rN = LsN/σN , rF = LsFσF /(4σ↑Fσ↓F ). (30)
From Eqs. (29) and (25) the current polarization can be
obtained as
Pj = [rcPΣ + rFPσF ] /rFN , (31)
where rFN = rF+rc+rN is the effective equilibrium resis-
tance of the F/N junction. It is important to emphasize
that a measured highly polarized current, representing
an efficient spin injection, does not itself imply a large
spin accumulation or a large density polarization, typi-
cally measured by optical techniques. In contrast to the
derivation of Pj from Eq. (31), determining Pn requires
using Poisson’s equation or a condition of the local charge
quasineutrality.41
It is useful to note42 that Eq. (31), written as Eq. (18)
in (Rashba, 2000) can be mapped to Eq. (A11) from
41 Carrier density will also be influenced by the effect of screen-
ing, which changes with the dimensionality of the spin injection
geometry (Korenblum and Rashba, 2002).
42 Rashba (2002a).

14
(Johnson and Silsbee, 1987), where it was first derived.43
An equivalent form for Pj in Eq. (31) was obtained by
Hershfield and Zhao (1997) and for rc = 0 results from
van Son et al. (1987) are recovered.
In contrast to normal metals (Johnson and Silsbee,
1985, 1988d) and superconductors, for which injection
has been reported in both conventional (Johnson, 1994),
and high temperature superconductors (Dong et al.,
1997; Hass et al., 1994; Vas’ko et al., 1997; Yeh et al.,
1999), creating a substantial current polarization
by direct electrical spin injection from a metal-
lic ferromagnet into a semiconductor proved to be
more difficult (Filip et al., 2000; Hammar et al., 1999;
Monzon and Roukes, 1999; Zhu et al., 2001).
By examining Eq. (31) we can both infer some possi-
ble limitations and deduce several experimental strate-
gies for effective spin injection i.e. to increase Pj into
semiconductors. For a perfect Ohmic contact rc = 0,
the typical resistance mismatch rF ≪ rN (where F is
a metallic ferromagnet) implies inefficient spin injection
with Pj ≈ rF /rN ≪ 1, referred to as the conductivity
mismatch problem by Schmidt et al. (2000). Even in the
absence of the resistive contacts, effective spin injection
into a semiconductor can be achieved if the resistance
mismatch is reduced by using for spin injectors either a
magnetic semiconductor or a highly spin-polarized ferro-
magnet.44
While there was early experimental evidence
(Alvarado and Renaud, 1992) that employing resis-
tive (tunneling) contacts could lead to an efficient spin
injection45 a systematic understanding was provided
by Rashba (2000) and supported with the subsequent
experimental and theoretical studies (Fert and Jaffres,
2001; Johnson, 2003; Johnson and Byers, 2003; Rashba,
2002c; Smith and Silver, 2001; Takahashi and Maekawa,
2003). As can be seen from Eq. (31) the spin-selective
resistive contact rc ≫ rF , rN (such as a tunnel or
Schottky contact) would contribute to effective spin
injection with Pj ≈ PΣ being dominated by the ef-
fect rc and not the ratio rF /rN .46 This limit is also
instructive to illustrate the principle of spin filtering
43 The substitutions are Pj → η∗, Pσ → p, PΣ → η, rc → [G(ξ −
η2)]−1, rN → δn/σnζn, rF → δf/σf (ζf − p2f ), LsN,F → δn,F ,
and n, f label N and F region, respectively. η, ζn, and ζf are of
the order of unity. To ensure that resistances and the spin diffu-
sion lengths in Johnson and Silsbee (1987) are positive, one must
additionally have (ξ − η2) > 0 and (ζi − p2i ) > 0, i = n, f (for
normal and ferromagnetic regions, respectively). In particular,
assuming ξ = ζn = ζf = 1 a detailed correspondence between
Eq. (31) and Eq. (A11) in (Johnson and Silsbee, 1987) is recov-
ered. For example, rc → [G(ξ − η2)]−1 yields Eq. (27), where
Σ → G.
44 From Eq. (30) a half-metallic ferromagnet implies a large rF .
45 The influence of the resistive contacts on spin injection can
also be inferred by explicitly considering resistive contacts
(Hershfield and Zhao, 1997; Johnson and Silsbee, 1987).
46 A similar result was stated previously by Johnson and Silsbee
(1988a).
(Esaki et al., 1967; Filip et al., 2002; Hao et al., 1990;
Moodera et al., 1988). In a spin-discriminating trans-
port process the resulting degree of spin polarization
is changed. Consequently the effect of spin filtering,
similar to spin injection, leads to the generation of
(nonequilibrium) spin polarization. 47 For example, at
low temperature EuS and EuSe, discussed in Sec. IV.C,
can act as spin-selective barriers. In the extreme case,
initially spin-unpolarized carriers (say, injected from a
nonmagnetic material) via spin-filtering could attain
a complete polarization. For a strong spin-filtering
contact PΣ > PσF , the sign of the spin accumulation
(nonequilibrium magnetization) is reversed in the F and
N regions, near the interface [recall Eq. (25)], in contrast
to the behavior sketched in Fig. 7, where µsF,N > 0.
The spin injection process alters the potential drop
across the F/N interface because differences of spin-
dependent electrochemical potentials on either side of the
interface generate an effective resistance δR. By integrat-
ing Eq. (20) for N and F regions, separately, it follows
that Rj = µN (0) − µF (0) + PσFµsF (0)/2, where R is
the junction resistance. Using Eqs. (26), (30), and (31)
allows us to express R = R0 + δR, where R0 = 1/Σ
(R0 = rc if Σ↑ = Σ↓) is the equilibrium resistance, in the
absence of spin injection, and
δR = [rN (rFP 2σF + rcP 2Σ) + rF rc(PσF − PΣ)2]/rFN ,(32)
where δR > 0 is the nonequilibrium resistance. Petukhov
has shown (Jonker et al., 2003a) that Eqs. (31) and (32)
could be obtained by considering an equivalent circuit
scheme with two resistors R˜↑, R˜↓ connected in par-
allel, where R˜λ = LsF /σλF + 1/Σλ + 2LsN/σN and
R˜↑ + R˜↓ = 4rFN . For such a resistor scheme, by not-
ing that j↑R˜↑ = j↓R˜↓, Eq. (31) is obtained as Pj =
−PR˜ ≡ −(R˜↑ − R˜↓)/(R˜↑ + R˜↓). δR in Eq. (32) is then
obtained as the difference between the total resistance
of the nonequilibrium spin-accumulation region of the
length LsF + LsN [given by the equivalent resistance
R˜↑R˜↓/(R˜↑ + R˜↓)] and the equilibrium resistance for the
same region, LsF /σF + LsN/σN .
The concept of the excess resistance δR can also
be explained as a consequence of the Silsbee-Johnson
spin-charge coupling Johnson and Silsbee (1985, 1987);
Silsbee (1980) and illustrated by considering the simpli-
fied schemes in Figs. 5 and 7. Accumulated spin near
the F/N interface, together with a finite spin relaxation
and a finite spin diffusion, impedes the flow of spins and
acts as a “spin bottleneck” (Johnson, 1991). A rise of
µsN must be accompanied by the rise of µsF [their pre-
cise alignment at the interface is given in Eq. (25)] or
there will be a backflow of the nonequilibrium spin back
47 While most of the schemes resemble a CPP geometry [Fig. 3(b)],
there are also proposals for generating highly polarized currents
in a CIP-like geometry [Fig. 3(a)] (Gurzhi et al., 2001, 2003).

18
through the depletion layer. There is no spin accumula-
tion. Spin injection appears only at large biases, where
it is driven by electric drift leading to nonequilibrium
spin population already in the n-region (Fabian et al.,
2002b; Zˇutic´ et al., 2002). In addition to spin injection,
spin extraction has also been predicted in magnetic p-n
junctions with a magnetic p-region (Zˇutic´ et al., 2002).
Under a large bias, spin is extracted (depleted) from the
nonmagnetic n-region.
Electric field in the bulk regions next to the space
charge is important only at large biases. It affects not
only spin density, but spin diffusion as well. That spin
injection efficiency can increase in the presence of large
electric fields due to an increase in the spin diffusion
length (spin drag) was first shown by Aronov and Pikus
(1976), and was later revisited by other authors.54 To
be important, the electric field needs to be very large,55
more than 100 V/cm at room temperature. While such
large fields are usually present inside the space-charge
regions, they exist in the adjacent bulk regions only at
the high injection limit and affect transport and spin
injection. In addition to electric drift, magnetic drift,
in magnetically inhomogeneous semiconductors, can also
enhance spin injection (Fabian et al., 2002b).
The following formula was obtained for spin injection
at small biases (Fabian et al., 2002b):
PLn =
PLn0[1− (PRn0)2] + δPRn (1− PLn0PRn0)
1− (PRn0)2 + δPRn (PLn0 − PRn0)
, (49)
where L (left) and R (right) label the edges of the space-
charge (depletion) region of a p-n junction. Correspond-
ingly, δPRn represents the nonequilibrium electron polar-
ization, evaluated at R, arising from a spin source. The
case discussed in Fig. 8 is for PLn0 = δPRn = 0. Then
PLn = 0, in accord with the result of no spin injection. For
a homogeneous equilibrium magnetization (PLn0 = PRn0),
δPLn = δPRn ; the nonequilibrium spin polarization is the
same across the depletion layer. Equation (49) demon-
strates that only nonequilibrium spin, already present in
the bulk region, can be transferred through the depletion
layer at small biases (Fabian et al., 2002b; Zˇutic´ et al.,
2001b). Spin injection of nonequilibrium spin is also very
effective if it proceeds from the p-region (Zˇutic´ et al.,
2001b), which is the case for a spin-polarized solar cell
(Zˇutic´ et al., 2001a). The resulting spin accumulation
in the n-region extends the spin diffusion range, lead-
ing to spin amplification—increase of the spin popula-
tion away from the spin source. These results were also
54 See, for example, (Bratkovsky and Osipov, 2003; Fabian et al.,
2002b; Flensberg et al., 2001; Margulis and Margulis, 1994;
Martin, 2003; Vignale and D’Amico, 2003; Yu and Flatte´, 2002a;
Zˇutic´ et al., 2001b).
55 The critical magnitude is obtained by dividing a typical energy,
such as the thermal or Fermi energy, by q and by the spin diffu-
sion length. At room temperature the thermal energy is 25 meV,
while the spin diffusion length can be several microns.
FIG. 9 Schematic top view of nonlocal, quasi-one-dimensional
geometry used by Johnson and Silsbee (1985): F1 and F2, the
two metallic ferromagnets having magnetizations in the x− z
plane; dotted lines, equipotentials characterizing electrical
current flow; grey shading, diffusing population of nonequilib-
rium spin-polarized electrons injected at x = 0, with darker
shades corresponding to higher density of polarized electrons.
From Johnson, 2002a.
confirmed in the junctions with two differently doped
n-regions (Pershin and Privman, 2003a,b). Note, how-
ever, that the term “spin polarization density” used in
Pershin and Privman (2003a,b) is actually the spin den-
sity s = n↑ − n↓, not the spin polarization Pn.
Theoretical understanding of spin injection has focused
largely on spin density while neglecting spin phase, which
is important for some proposed spintronic applications.
The problem of spin evolution in various transport modes
(diffusion, tunneling, thermionic emission) remains to
be investigated. Particularly relevant is the question of
whether spin phase is conserved during spin injection.
Malajovich et al. (2001) showed, by studying spin evolu-
tion in transport through a n-GaAs/n-ZnSe heterostruc-
ture, that the phase can indeed be preserved.
D. Experiments on spin injection
1. Johnson-Silsbee spin injection
The first spin polarization of electrons by electrical spin
injection (Johnson and Silsbee, 1985) was demonstrated
in a “bulk wire” of aluminum on which an array of thin
film permalloy (Py) pads (with 70 % nickel and 30 %
iron) was deposited spaced in multiples of 50 µm, center
to center (Johnson and Silsbee, 1988d) to serve as spin
injectors and detectors. In one detection scheme a single
ferromagnetic pad was used as a spin injector while the
distance to the spin detector was altered by selecting dif-
ferent Py pads to detect Vs and through the spatial decay
of this spin-coupled voltage infer LsN .56 This procedure
is illustrated in Fig. 9, where the separation between the
56 The spin relaxation time in a ferromagnet is often assumed to be
very short. Correspondingly, in the analysis of the experimental
data, both the spin diffusion length and δM are taken to vanish in
the F region (Johnson and Silsbee, 1985, 1988a,d; Silsbee, 1980).

19
FIG. 10 Spin injection data from bulk Al wire sample. Neg-
ative magnetic field is applied parallel to the magnetization
(-z axis) in the two ferromagnetic regions. As the field is
increased, at B0,1 magnetization in one of the ferromagnetic
regions is reversed, and at B0,2 the magnetization in the other
region is also reversed (both are along +z axis). Inset: ampli-
tude of the observed Hanle signal as a function of orientation
angle φ of magnetic field. From Johnson and Silsbee, 1985.
spin injector and detector Lx is variable.
Johnson and Silsbee (1985) point out that in the de-
picted geometry there is no flow of the charge current for
x > 0 and that in the absence of nonequilibrium spins a
voltage measurement between x = Lx and x = b gives
zero. Injected spin-polarized electrons will diffuse sym-
metrically (at low current density the effect of electric
fields can be neglected), and the measurement of voltage
will give a spin-coupled signal Vs related to the relative
orientation of magnetizations in F1 and F2.57 The re-
sults, corresponding to the polarizer-analyzer detection
and the geometry of Fig. 9, are given in Fig. 10. An in-
plane field (B ‖ zˆ), of a magnitude several times larger
than a typical field for magnetization reversal, B0 ≈ 100
G, is applied to define the direction of magnetization in
the injector and detector. As the field sweep is per-
formed, from negative to positive values, at B01 there
is a reversal of magnetization in one of the ferromagnetic
films accompanied by a sign change in the spin-coupled
signal. As Bz is further increased, at approximately B02,
there is another reversal of magnetization, resulting in
parallel orientation of F1 and F2 and a Vs of magnitude
similar to that for the previous parallel orientation when
Bz < B01.
A more effective detection of the spin injection is re-
alized through measurements of the Hanle effect, also
discussed Secs. II.B and III.A.2, and described by the
Bloch-Torrey equations (Bloch, 1946; Torrey, 1956) [see
Eqs.( 52)–(54)]. The inset of Fig. 10 summarizes results
from a series of Hanle experiments on a single sample.
For the Hanle effect B must have a component perpen-
dicular to the orientation axes of the injected spins. Only
projection of B perpendicular to the spin axis applies a
57 This method for detecting the effects of spin injection is also
referred to as a potentiometric method.
torque and dephases spins. The magnitude of B, ap-
plied at an angle φ to the z-axis in the y − z plane,
is small enough that the magnetizations in ferromag-
netic thin films remain in the x − z plane (see Fig. 9).
If, at B = 0, injected nonequilibrium magnetization is
δM(0)zˆ then at finite field δM precesses about B with
the cone of angle 2φ. After averaging over several cy-
cles, only δM(0) cosφ, the component ‖ B, will sur-
vive. The voltage detector58 senses the remaining part of
the magnetization projected on the axis of the detector
δM(0) cosφ × cosφ (Johnson and Silsbee, 1988a). The
predicted angular dependence for the amplitude of the
Hanle signal (proportional to the depolarization of δM
in a finite field) [δM(0)− δM(0) cos2 φ] is plotted in the
inset together with the measured data.59 Results con-
firm the first application of the Hanle effect to dc spin
injection.
The Hanle effect was also studied theoretically by solv-
ing the Bloch-Torrey equations for an arbitrary orienta-
tion, characterized by the angle α, between the magneti-
zation in F1 and F2 (Johnson and Silsbee, 1988a). From
the Hanle curve [Vs(B⊥)] measured at T = 4.3 (36.6) K,
the parameters Ls = 450 (180) µm and PΣ = 0.06 (0.08)
were extracted.60 This spin injection technique using a
few pV resolution of a superconducting quantum interfer-
ence device (SQUID) and with an estimated PΣ ≈ 0.07
provided an accuracy able to detect Pn ≈ 5×10−12, caus-
ing speculating on that a single-spin sensitivity might be
possible in smaller samples (Johnson and Silsbee, 1985,
1988d). While in a good conductor, such as Al, the ob-
served resistance change ∆R was small (∼ nΩ), the rel-
ative change at low temperatures and for Lx ≪ Ls was
∆R/R ≈ 5%, where ∆R is defined as in Eq. (1), deter-
mined by the relative orientation of the magnetization
in F1 and F2, and R is the Ohmic resistance (Johnson,
2002a). Analysis from Sec. II.C.2 shows that the mea-
surement of ∆R could be used to determine the product
of injected current polarizations in the two F/N junc-
tions.
The studies of spin injection were extended to the thin-
film geometry, also known as the “bipolar spin switch”
or “Johnson spin transistor” (Johnson, 1993a,b) similar
to the one depicted in Fig. 5(a). The measured spin-
coupled signals 61 in Au films were larger than the values
obtained in bulk Al wires (Johnson and Silsbee, 1985,
1988d). A similar trend, Vs ∼ 1/d, potentially impor-
58 Recall from the discussion leading to Eq. (39) that the spin-
coupled signal ∝ δM .
59 The range of the angle φ, in the inset, is corrected from the one
originally given in Fig. 3 of Johnson and Silsbee (1985).
60 The fitting parameters are τs, PΣ, and α (Johnson and Silsbee,
1988d), and since the diffusion coefficient is obtained from Ein-
stein’s relation Ls is known.
61 d ∼ 100 nm was much smaller then the separation between F1
and F2 in bulk Al wires (Johnson and Silsbee, 1985), and the
amplitude of the Hanle effect was about 104 larger (Johnson,
2002a).

26
∂My
∂t = γ(M×B)y −
My
T2
+D∇2My, (53)
∂Mz
∂t = γ(M×B)z −
Mz −M0z
T1
+D∇2Mz. (54)
Here γ = µBg/h¯ is the electron gyromagnetic ratio (µB
is the Bohr magneton and g is the electronic g factor),
D is the diffusion coefficient (for simplicity we assume an
isotropic or a cubic solid with scalar D), and M0z = χB0
is the thermal equilibrium magnetization with χ denoting
the system’s static susceptibility. The Bloch equations
are phenomenological, describing quantitatively very well
the dynamics of mobile electron spins (more properly,
magnetization) in experiments such as conduction elec-
tron spin resonance and optical orientation. Although
relaxation and decoherence processes in a many-spin sys-
tem are generally too complex to be fully described by
only two parameters, T1 and T2 are nevertheless an ex-
tremely robust and convenient measure for quantifying
such processes in many cases of interest. To obtain
microscopic expressions for spin relaxation and dephas-
ing times, one starts with a microscopic description of
the spin system (typically using the density-matrix ap-
proach), derives the magnetization dynamics, and com-
pares it with the Bloch equations to extract T1 and T2.
Time T1 is the time it takes for the longitudinal mag-
netization to reach equilibrium. Equivalently, it is the
time of thermal equilibration of the spin population with
the lattice. In T1 processes an energy has to be taken
from the spin system, usually by phonons, to the lattice.
Time T2 is classically the time it takes for an ensemble
of transverse electron spins, initially precessing in phase
about the longitudinal field, to lose their phase due to
spatial and temporal fluctuations of the precessing fre-
quencies. For an ensemble of mobile electrons the mea-
sured T1 and T2 come about by averaging spin over the
thermal distribution of electron momenta. Electrons in
different momentum states have not only different spin-
flip characteristics, but also slightly different g factors
and thus different precession frequency. This is analo-
gous to precession frequencies fluctuations of localized
spins due to inhomogeneities in the static field B0. How-
ever, since momentum scattering (analogous to inter-
site hopping or exchange interaction of localized spins)
typically proceeds much faster than spin-flip scattering,
the g-factor-induced broadening is inhibited by motional
narrowing70 and need not be generally considered as
contributing to T2 [see, however, (Dupree and Holland,
70 Motional (dynamical) narrowing is an inhibition of phase change
by random fluctuations (Slichter, 1989). Consider a spin rotating
with frequency ω0. The spin phase changes by ∆φ = ω0t over
time t. If the spin is subject to a random force that makes spin
precession equally likely clockwise and anticlockwise, the aver-
age spin phase does not change, but the root-mean-square phase
change increases with time as (〈∆2φ〉)1/2 ≈ (ω0τc)(t/τc)1/2,
where τc is the correlation time of the random force, or the av-
erage time of spin precession in one direction. This is valid for
1967)]. Indeed, motional narrowing of the g-factor fluc-
tuations, δg, gives a contribution to 1/T2 of the order
of ∆ω2τp, where the B0-dependent precession frequency
spread is ∆ω = (δg/g)γB0 and τp is the momentum scat-
tering time. For B0 fields of the order 1 T, scattering
times of 1 ps, and δg as large as 0.01, the “inhomogeneous
broadening” is a microsecond, which is much more than
the observed values for T2. Spatial inhomogeneities of
B0, like those coming from hyperfine fields, are inhibited
by motional narrowing, too, due to the itinerant nature
of electrons. For localized electrons (e.g., for donor states
in semiconductors), spatial inhomogeneities play an im-
portant role and are often observed to affect T2. To de-
scribe such reversible phase losses, which can potentially
be eliminated by spin-echo experiments, sometimes the
symbol T ∗2 (Hu et al., 2001b) is used to describe spin
dephasing of ensemble spins, while the symbol T2 is re-
served for irreversible loss of the ensemble spin phase. In
general, T ∗2 ≤ T2, although for conduction electrons to a
very good approximation T ∗2 = T2.
In isotropic and cubic solids T1 = T2 if γB0 ≪ 1/τc,
where τc is the so-called correlation or interaction time:
1/τc is the rate of change of the effective dephasing
magnetic field (see footnote 70). Phase losses occur
during time intervals of τc. As shown below, in elec-
tronic systems τc is given either by τp or by the time
of the interaction of electrons with phonons and holes.
Those times are typically smaller than a picosecond, so
T1 = T2 is fulfilled for magnetic fields up to several
tesla. The equality between the relaxation and dephas-
ing times was noticed first in the context of NMR (Bloch,
1946; Wangsness and Bloch, 1953) and later extended
to electronic spin systems (Andreev and Gerasimenko,
1958; Pines and Slichter, 1955). A qualitative reason for
T1 = T2 is that if the phase acquires a random contri-
bution during a short time interval τc, the energy un-
certainty of the spin levels determining the longitudinal
spin is greater than the Zeeman splitting h¯γB0 of the lev-
els. The splitting then does not play a role in dephasing,
and the dephasing field will act equally on the longitu-
dinal and transverse spin. In classical terms, spin that
is oriented along the direction of the magnetic field can
precess a full period about the perpendicular fluctuating
field, feeling the same dephasing fields as transverse com-
ponents. As the external field increases, the precession
angle of the longitudinal component is reduced, inhibit-
ing dephasing.
The equality of the two times is very convenient for
comparing experiment and theory, since measurements
usually yield T2, while theoretically it is often more con-
venient to calculate T1. In many cases a single symbol τs
is used for spin relaxation and dephasing (and called in-
rapid fluctuations, ω0τc ≪ 1. The phase relaxation time tφ is
defined as the time over which the phase fluctuations reach unity:
1/tφ = ω20τc.

28
trode detects the amount of spin as a position-dependent
quantity. The detection is by means of spin-charge cou-
pling, whereby an EMF appears across the paramag-
net/ferromagnet interface in proportion to the nonequi-
librium magnetization (Silsbee, 1980). By fitting the spa-
tial dependence of magnetization to the exponential de-
cay formula, one can extract the spin diffusion length Ls
and thus the spin relaxation time T1 = L2s/D. The Hanle
effect, too, can be used in combination with Johnson-
Silsbee spin injection, yielding directly T1 = T2, which
agrees with T1 determined from the measurement of Ls.
A precursor to the Hanle effect in spin injection was
transmission-electron spin resonance (TESR), in which
nonequilibrium electron spin excited in the skin layer of
a metallic sample is transported to the other side, emit-
ting microwave radiation. In very clean samples and
at low temperatures, electrons ballistically propagating
through the sample experience Larmor precession result-
ing in Larmor waves, seen as an oscillation of the trans-
mitted radiation amplitude with changing static mag-
netic field (Ja´nossy, 1980).
Time-resolved photoluminescence detects, after cre-
ation of spin-polarized carriers, circular polarization of
the recombination light. This technique was used, for
example, to detect a 500 ps spin coherence time T2 of
free excitons in a GaAs quantum well (Heberle et al.,
1994). The Faraday and (magneto-optic) Kerr effects are
the rotation of the polarization plane of a linearly polar-
ized light, transmitted through (Faraday) or reflected by
(Kerr) a magnetized sample. The Kerr effect is more
useful for thicker and nontransparent samples or for thin
films fabricated on thick substrates. The angle of rota-
tion is proportional to the amount of magnetization in
the direction of the incident light. Pump (a circularly
polarized laser pulse) and probe experiments employing
magneto-optic effects can now follow, with 100 fs resolu-
tion, the evolution of magnetization as it dephases in a
transverse magnetic field. Using lasers for spin excitation
has the great advantage of not only detecting, but also
manipulating spin dephasing, as shown using Faraday
rotation on bulk GaAs and GaAs/ZnSe heterostructures
(Awschalom and Kikkawa, 1999; Kikkawa et al., 2001).
The Kerr effect was used, for example, to investigate the
spin dynamics of bulk CdTe (Kimel et al., 2000), and
Faraday rotation was used to study spin coherence in
nanocrystals of CdSe (Gupta et al., 2002) and coherent
control of spin dynamics of excitons in GaAs quantum
wells (Heberle et al., 1996).
B. Mechanisms of spin relaxation
Four mechanisms for spin relaxation of conduction
electrons have been found relevant for metals and semi-
conductors: the Elliott-Yafet (EY), D’yakonov-Perel’
(DP), Bir-Aronov-Pikus (BIP), and hyperfine-interaction
(HFI) mechanisms.73 In the EY mechanism electron
spins relax because the electron wave functions normally
associated with a given spin have an admixture of the
opposite spin states, due to spin-orbit coupling induced
by ions. The DP mechanism explains spin dephasing
in solids without a center of symmetry. Spin dephasing
occurs because electrons feel an effective magnetic field,
resulting from the lack of inversion symmetry and from
the spin-orbit interaction, which changes in random di-
rections every time the electron scatters to a different
momentum states. The BIP mechanism is important for
p-doped semiconductors, in which the electron-hole ex-
change interaction gives rise to fluctuating local magnetic
fields flipping electron spins. Finally, in semiconduc-
tor heterostructures (quantum wells and quantum dots)
based on semiconductors with a nuclear magnetic mo-
ment, it is the hyperfine interaction of the electron spins
and nuclear moments which dominates spin dephasing of
localized or confined electron spins. An informal review
of spin relaxation of conduction electrons can be found
in Fabian and Das Sarma (1999c).
1. Elliott-Yafet mechanism
Elliott (1954) was the first to realize that conduction-
electron spins can relax via ordinary momentum scatter-
ing (such as by phonons or impurities) if the lattice ions
induce spin-orbit coupling in the electron wave function.
In the presence of the spin-orbit interaction
Vso =
h¯
4m2c2∇Vsc × pˆ · σˆ, (55)
where m is the free-electron mass, Vsc is the scalar (spin-
independent) periodic lattice potential, pˆ ≡ −ih¯∇ is the
linear momentum operator, and σˆ are the Pauli matri-
ces, single-electron (Bloch) wave functions in a solid are
no longer the eigenstates of σˆz , but rather a mixture of
the Pauli spin up | ↑〉 and spin down | ↓〉 states. If the
solid possesses a center of symmetry, the case of elemen-
tal metals which Elliott considered, the Bloch states of
“spin up” and “spin down” electrons with the lattice mo-
mentum k and band index n can be written as (Elliott,
1954)
Ψkn↑(r) = [akn(r)| ↑〉+ bkn(r)| ↓〉] eik·r, (56)
Ψkn↓(r) =
[
a∗−kn(r)| ↓〉 − b∗−kn(r)| ↑〉
]
eik·r, (57)
where we write the explicit dependence of the complex
lattice-periodic coefficients a and b on the radius vec-
tor r. The two Bloch states are degenerate: they are
connected by spatial inversion and time reversal (Elliott,
73 We do not consider magnetic scattering, that is, scattering due to
an exchange interaction between conduction electrons and mag-
netic impurities.

31
Two limiting cases can be considered: (i) τpΩav >∼ 1
and (ii) τpΩav <∼ 1, where Ωav is an average magnitude of
the intrinsic Larmor frequency Ω(k) over the actual mo-
mentum distribution. Case (i) corresponds to the situa-
tion in which individual electron spins precess a full cycle
before being scattered to another momentum state. The
total spin in this regime initially dephases reversibly due
to the anisotropy in Ω(k). The spin dephasing rate,75
which depends on the distribution of values of Ω(k), is
in general proportional to the width ∆Ω of the distribu-
tion: 1/τs ≈ ∆Ω. The spin is irreversibly lost after time
τp, when randomizing scattering takes place.
Case (ii) is what is usually meant by the D’yakonov-
Perel’ mechanism. This regime can be viewed from the
point of view of individual electrons as a spin preces-
sion about fluctuating magnetic fields, whose magnitude
and direction change randomly with the average time
step of τp. The electron spin rotates about the intrin-
sic field at an angle δφ = Ωavτp, before experiencing an-
other field and starting to rotate with a different speed
and in a different direction. As a result, the spin phase
follows a random walk: after time t, which amounts
to t/τp steps of the random walk, the phase progresses
by φ(t) ≈ δφ
√
t/τp. Defining τs as the time at which
φ(t) = 1, the usual motional narrowing result is obtained:
1/τs = Ω2avτp (see footnote 70). The faster the momen-
tum relaxation, the slower the spin dephasing. The dif-
ference between cases (i) and (ii) is that in case (ii) the
electron spins form an ensemble that directly samples
the distribution of Ω(k), while in case (ii) it is the dis-
tribution of the sums of the intrinsic Larmor frequencies
(the total phase of a spin after many steps consists of a
sum of randomly selected frequencies multiplied by τp),
which, according to the central limit theorem, has a sig-
nificantly reduced variance. Both limits (i) and (ii) and
the transition between them have been experimentally
demonstrated in n-GaAs/AlGaAs quantum wells by ob-
serving temporal spin oscillations over a large range of
temperatures (and thus τp) (Brand et al., 2002).
A more rigorous expression for τs in regime (ii) has
been obtained by solving the kinetic rate equation for
a spin-dependent density matrix (D’yakonov and Perel’,
1971d,e). If the band structure is isotropic and scattering
is both elastic and isotropic, evolution of the z-component
of spin s is (Pikus and Titkov, 1984)
s˙z = −τ˜l
[
sz(Ω2 − Ω2z)− sxΩxΩz − syΩyΩz
]
, (68)
where the bar denotes averaging over directions of k.
Analogous expressions for s˙x and s˙y can be written by
index permutation. The effective momentum scattering
time is introduced as
1/τ˜l =
∫ 1
−1
W (θ) [1− Pl (cos θ)] d cos θ, (69)
75 The reversible decay need not be exponential.
where W (θ) is the rate of momentum scattering through
angle θ at energy Ek, and Pl is the Legendre polynomial
whose order l is the power of k in Ω(k). [It is assumed
that Ω(k) ∼ kl in Eq. (68).] In two dimensions Pl(cos θ)
is replaced by cos(lθ) in Eq. (69) for the lth polar har-
monic ofΩ(k) (Pikus and Pikus, 1995). Since it is useful
to express the results in terms of the known momentum
relaxation times76 τp = τ˜1, one defines 77 γl = τp/τ˜l to
measure the effectiveness of momentum scattering in ran-
domizing Larmor frequencies; τ˜l accounts for the relative
angle between Ω before and after scattering. Generally
γl > 1 for l > 1, that is, momentum scattering is more
effective in randomizing spins than in randomizing mo-
mentum.
Comparing with the Bloch-Torrey equations (52)–(54),
for B = 0 and no spin diffusion, we see that spin decay is
described by the tensor 1/τs,ij (here i and j are the Carte-
sian coordinates) whose diagonal 1/τs,ii and off-diagonal
1/τs,ij , for i 6= j, terms are
1/τs,ii = γ−1l τp(Ω2 − Ω2i ), 1/τs,ij = −γ−1l τpΩiΩj . (70)
In general, spin dephasing depends on the spin direc-
tion and on the dephasing rates of the perpendicular spin
components. Equations (70) are valid for small magnetic
fields, satisfying Ω0τp ≪ 1, where Ω0 is the Larmor fre-
quency of the external field.
The most important difference between the EY and the
DP mechanism is their opposite dependence on τp. While
increased scattering intensity makes the EY mechanism
more effective, it decreases the effectiveness of the the
DP processes. In a sense the two mechanisms are similar
to collision broadening and motional narrowing in NMR
(Slichter, 1989). Indeed, in the EY process the precession
frequency is conserved between collisions and the loss of
phase occurs only in the short time during collision. The
more collisions there are, the greater is the loss of phase
memory, in analogy with collision broadening of spectral
lines. On the other hand, in DP spin dephasing, spin
phases are randomized between collisions, since electrons
precess with different frequencies depending on their mo-
menta. Spin-independent collisions with impurities or
phonons do not lead to phase randomization during the
collision itself, but help to establish the random-walk-like
evolution of the phase, leading to motional narrowing.
While these two mechanisms coexist in systems lacking
inversion symmetry, their relative strength depends on
many factors. Perhaps the most robust trend is that the
DP mechanism becomes more important with increasing
band gap and increasing temperature.
76 In fact, normal (not umklapp) electron-electron collisions should
also be included in the effective spin randomization time τ˜ ,
though they do not contribute to the momentum relaxation time
which appears in the measured mobility (Glazov and Ivchenko,
2002, 2003).
77 Pikus and Titkov (1984) initially define γl as here, but later eval-
uate it, inconsistently, as the inverse γl → γ−1l .

34
As for the [001] case, a perpendicular spin dephases twice
as fast as a parallel one, since Ω(k) lies in the plane.
The most interesting case is the [110] orientation for
which 1/τs,xx = 1/τs,yy = 1/2τs,zz = −1/τs,xy = 1/8τ0s .
Other off-diagonal components vanish. Diagonalizing the
tensor gives
1/τs,‖ = 1/4τ0s , 1/τs,⊥ = 0. (86)
The perpendicular spin does not dephase. This is due
to the fact that κ, unlike the previous cases, is always
normal to the plane (see Fig. 15), and thus cannot affect
the precession of the perpendicular spin. Indeed,
Ω(k) ∼ κ = k2n (kx/2)(−1,−1, 0) , (87)
where it is used that k · n = 0. Spin dephasing in [110]
QW’s can still be due to the cubic terms in k left out of
Eq. (77) or to other spin relaxation mechanisms. Note
that the magnitude of Ω(k) changes along the Fermi sur-
face. Electrons moving along [001] experience little spin
dephasing.
The structure inversion asymmetry term
arises from the Bychkov-Rashba spin splitting
(Bychkov and Rashba, 1984a,b; Rashba, 1960) oc-
curring in asymmetric QW’s or in deformed bulk
systems. The corresponding Hamiltonian is that of
Eq. (67), with the precession vector
Ω(k) = 2αBR(k× n). (88)
Here αBR is a parameter depending on spin-orbit cou-
pling and the asymmetry of the confining electrostatic
potentials arising from the growth process of the het-
erostructure. The splitting can also arise in nominally
symmetric heterostructures with fluctuations in doping
density (Sherman, 2003b). The Bychkov-Rashba field
always lies in the plane, having a constant magnitude.
As for the bulk inversion asymmetry case, the struc-
ture inversion asymmetry leads to a splitting of the
Fermi surface, according to the direction of the spin
pattern—parallel or antiparallel to Ω(k), as shown in
Fig. 15. Perhaps the most appealing fact about struc-
ture inversion asymmetry is that αBR can be tuned
electrostatically, potentially providing an effective spin
precession control without the need for magnetic fields
(Levitov and Rashba, 2003; Rashba and Efros, 2003).
This has led to one of the pioneering spintronic propos-
als by Datta and Das (1990) (see Sec. IV.E.1). Note that
for the [111] orientation the bulk and structure inversion
asymmetry terms have the same form.
Using the same procedure as for bulk inversion asym-
metry, we describe the spin relaxation rate by Eq. (78)
as
1/τ0s = 4α2BR
mc
h¯2
Ekτp (89)
and
νij = 1− ninj. (90)
Since the intrinsic precession vector ∼ Ω(k) for the struc-
ture inversion asymmetry always lies in the plane, a per-
pendicular spin should dephase twice as fast as a spin in
the plane. Indeed, by diagonalizing 1/τs,ij one finds that
1/τs,‖ = 1/2τs,⊥ = 1/τ0s (91)
holds for all QW orientations n. This interesting fact
qualitatively distinguishes structure from bulk inversion
asymmetry and can be used in assessing the relative im-
portance of the Dresselhaus and Rashba spin splittings
in III-V heterostructure systems. If bulk and structure
inversion asymmetry are of similar importance, the in-
terference terms from the cross product ΩBIAΩSIA can
lead to spin dephasing anisotropies within the plane,
as was shown for [001] QW’s in (Averkiev and Golub,
1999; Kainz et al., 2003). This plane anisotropy can be
easily seen by adding the corresponding vector fields in
Fig. 15. Another interesting feature of bulk and struc-
ture inversion asymmetry fields is that injection of elec-
trons along a quasi-one-dimensional channel can lead
to large relaxation times for spins oriented along Ω(k),
where k is the wave vector for the states in the channel
(Hammar and Johnson, 2002).
Model spin dephasing calculations based on
structure inversion asymmetry were carried out by
Pareek and Bruno (2002). Calculations of τs based on
the DP mechanism, with structural asymmetry due to
doping fluctuations in the heterostructure interface were
performed by Sherman (2003b).
Research on spin inversion asymmetry is largely mo-
tivated by Datta-Das spin field-effect transistor proposal
(see Secs. I.A and IV.E.1) in which αBR is tailored by a
gate. This tailoring, however, has been controversial and
the microscopic origin of the Bychkov-Rashba Hamilto-
nian, and thus the interpretation of experimental results
on splitting in semiconductor heterostructures, has been
debated. The Bychkov-Rashba Hamiltonian is often in-
terpreted as arising from the electric field of the confin-
ing potential, assisted by external bias, which acts on
a moving electron in a transverse direction. The rela-
tivistic transformation then gives rise to a magnetic field
(spin-orbit coupling) acting on the electron spin. The pa-
rameter αBR is then assumed to be directly proportional
to the confining electrical field. This is in general wrong,
since the average electric force acting on a confined par-
ticle of uniform effective mass is zero.
The asymmetry that gives rise to structure inversion
asymmetry is the asymmetry in the band structure (in-
cluding spin-orbit coupling) parameters of a heterostruc-
ture, such as the effective mass, or the asymmetry in
the penetration of the electron wave function into the
barriers (de Andrada e Silva et al., 1997). The difficulty
in understanding the influence of the external gates is
caused by the lack of the understanding of the influence
of the gate field on the asymmetry of the well. For a
clear qualitative explanation of the involved physics see
Pfeffer and Zawadzki (1999) and Zawadzki and Pfeffer
(2001). Band-structure k · p calculations of αBR for

35
quantum wells in GaAs/AlGaAs heterostructures can
be found in Pfeffer and Zawadzki (1995), Pfeffer (1997),
Wissinger et al. (1998), and Kainz et al. (2003); a cal-
culation for InGaAs/InP quantum wells is reported
in Engels et al. (1997) and Scha¨pers et al. (1998), in
InSb/InAlSb asymmetric quantum well it can be found in
Pfeffer and Zawadzki (2003), and in p-InAs metal-oxide-
semiconductor field-effect transistor channel in Lamari
(2003). Adding to the controversy, Majewski and Vogl
(2003) have recently calculated the structure inversion
asymmetry by local density functional methods and con-
cluded that the induced spin splitting arises from micro-
scopic electric fields in asymmetric atomic arrangements
at the interfaces, so that a large Bychkov-Rashba term
can be present in otherwise symmetric quantum wells
with no common atom.
Interpretation of experimental data on structure in-
version asymmetry is difficult, especially at determin-
ing the zero magnetic field spin splitting (usually seen
in Shubnikov- de Haas oscillations), which is masked by
Zeeman splitting at finite fields. In addition, the split-
tings are small, typically less than 1 meV. The Bychkov-
Rashba parameter was measured in GaSb/InAs/GaSb
quantum wells (αBR ≈ 0.9× 10−11 eV m for 75 A˚ thick
well) by Luo et al. (1990); in InAlAs/InGaAs/InAlAs
quantum wells (20 nm), where also the gate voltage is
obtained: αBR ranged from 10−11 eV m at the deplet-
ing voltage of -1 V, to 5× 10−12 eV m at +1.5 V. Weak
antilocalization studies of InAlAs/InGaAs/InAlAs quan-
tum wells have recently been used to study electron den-
sity dependence of αBR by Koga et al. (2002a). Gate
dependence of αBR was also measured in modulation-
doped InP/InGaAs/InP quantum wells (Engels et al.,
1997; Scha¨pers et al., 1998). The observed values are
several 10−12 eV m. On the other hand, there are exper-
imental reports that either fail to observe the expected
spin splitting due to Bychkov-Rashba field, or interpret
the splitting differently [see, for example, Brosig et al.
(1999) and Rowe et al. (2001)]. Furthermore, measure-
ments of Heida et al. (1998) show a constant αBR ≈
0.6× 10−11 eV m, independent of gate voltage, in asym-
metric AlSb/InAS/AlSb quantum wells, demonstrating
that control of αBR may be difficult. In order to unify
the different views on what exactly the Bychkov-Rashba
spin splitting means and how the spin splitting can be
tuned with gate voltage, more experimental efforts need
to be devoted to this interesting topic.
3. Bir-Aronov-Pikus Mechanism
Spin relaxation of conduction electrons in p-doped
semiconductors can also proceed through scattering, ac-
companied by spin exchange, by holes, as was first shown
by Bir et al. (1975).
The exchange interaction between electrons and holes
is governed by the Hamiltonian
H = AS · Jδ(r), (92)
where A is proportional to the exchange integral between
the conduction and valence states, J is the angular mo-
mentum operator for holes, S is the electron spin opera-
tor, and r is the relative position of electrons and holes.
The spin-flip scattering probability depends on the
state of the holes (degenerate or nondegenerate, bound
on acceptors or free, fast or slow). We present below the
most frequently used formulas when assessing the rele-
vance of the BAP mechanism. The formulas are valid
for the usual cases of heavy holes mv ≫ mc. For elec-
tron spin relaxation due to exchange with nondegenerate
holes,
1
τs
=
2
τ0
Naa3B
vk
vB
[ p
Na
|ψ(0)|4 + 5
3
Na − p
Na
]
, (93)
where aB is the exciton Bohr radius aB = h¯2ǫ/e2mc,
p is the density of free holes, τ0 is an exchange split-
ting parameter: h¯/τ0 = (3π/64)∆2ex/EB (with EB de-
noting the Bohr exciton energy, EB = h¯2/2mca2B and
∆ex the exchange splitting of the excitonic ground state),
and vB = h¯/mcaB; |ψ(0)|2 is Sommerfeld’s factor, which
enhances the free hole contribution. For an unscreened
Coulomb potential
|ψ(0)|2 = 2πκ
[
1− exp
(
−2πκ
)]−1
, (94)
where κ = Ek/EB. For a completely screened potential
|ψ(0)|2 = 1.
If holes are degenerate and the electrons’ velocity vk is
greater than the Fermi velocity of the holes’, then
1
τs
=
3
τ0
pa3B
vk
vB
kBT
EFh
, (95)
where EFh is the hole Fermi energy. For degenerate
holes |ψ(0)|2 is of order 1. If electrons are thermal-
ized, vk needs to be replaced by the thermal velocity
ve = (3kBT/mc)1/2.
The temperature dependence of τs is dominated by
the temperature dependence of |ψ(0)|2 as well as by p.
The dependence on the acceptor density is essentially
1/τs ∼ Na for nondegenerate/bound holes from Eq. (93)
and 1/τs ∼ N1/3a for degenerate holes from Eq. (95). In
between, 1/τs is only weakly dependent onNa. For GaAs
aB ≈ 114 A˚, EB ≈ 4.9 meV, vB ≈ 1.7 × 107 cm·s−1,
τ0 ≈ 1×10−8 s, and ∆ex ≈ 4.7×10−5 eV (Aronov et al.,
1983).
The BAP mechanism coexists with the the EY and
DP mechanisms in p-doped materials lacking inversion
symmetry. The three mechanisms can be distinguished
by their unique density and temperature dependences.
A general trend is that the BAP dominates in heavily
doped samples at small temperatures. At large temper-
atures even for large acceptor densities, the DP mecha-
nism can become more important, due to its increased
importance at large electron energies. Specific examples
of the domain of importance for the three mechanisms are

36
discussed in Sec. III.D.1. Model calculations of BAP pro-
cesses for electrons in p-doped bulk and quantum wells
were performed by Maialle (1996); Maialle and Degani
(1997).
Another potentially relevant mechanism for spin re-
laxation of donor-bound electrons in p-doped semicon-
ductors is the exchange interaction with holes bound to
acceptors (D’yakonov and Perel’, 1973b). The exchange
interaction provides an effective magnetic field for elec-
tron spins to precess, leading to inhomogeneous dephas-
ing. Both electron hopping and hole spin-flip motionally
narrow the precession.
4. Hyperfine-interaction mechanism
The hyperfine interaction, which is the magnetic
interaction between the magnetic moments of elec-
trons and nuclei, provides an important mecha-
nism (D’yakonov and Perel’, 1973b) for ensemble spin
dephasing and single-spin decoherence of localized elec-
trons, such as those confined in quantum dots (QD)
or bound on donors. The interaction is too weak to
cause effective spin relaxation of free electrons in met-
als or in bulk semiconductors (Overhauser, 1953a), as it
is strongly dynamically narrowed by the itinerant nature
of electrons (see Sec. III.A.1). In addition to spin dephas-
ing, the hyperfine interaction is relevant for spintronics
as a means to couple, in a controlled way, electron and
nuclear spins (D’yakonov and Perel’, 1984a).
Localized electrons are typically spread over many lat-
tice sites (104–106), experiencing the combined magnetic
moments of many nuclei. In GaAs all the lattice nu-
clei carry the magnetic moment of 3/2 spin, while in Si
the most abundant isotope, 28Si, carries no spin and the
hyperfine interaction is due to 29Si (natural abundance
4.67%) or the frequent donor 31P, both of nuclear spin
1/2. As a result, an electron bound on a shallow donor
in Si experiences only around 100 magnetic nuclei, and
the effects of the hyperfine interaction are considerably
smaller than in GaAs.
The effective Hamiltonian for the hyperfine interaction
is the Fermi contact potential energy (Slichter, 1989)
H = 8π
3
µ0
4πg0µB
∑
i
h¯γn,iS · Iiδ(r−Ri), (96)
where µ0 is the vacuum permeability, g0 = 2.0023 is the
free-electron g factor, µB is the Bohr magneton, i is the
label for nuclei at positionsRi, S, and Ii are, respectively,
electron and nuclear spin operators expressed in the units
of h¯, and γn,i is the nuclear gyromagnetic ratio. We stress
that it is the electron g factor g0 and not the effective g
that appears in the hyperfine interaction, Eq. (96), as
shown by Yafet (1961) [see also Paget et al. (1977)]. It
follows that the spin of an electron in an orbital state
ψ(r) experiences magnetic field
Bn =
2µ0
3
g0
g
∑
i
h¯γn,iIi|ψ(Ri)|2, (97)
where g is the effective g factor of the electron. The
electron Zeeman splitting due to the average Bn corre-
sponds to a field of ∼ 1 T or thermal energy of 1 K, for
a complete nuclear polarization (Paget et al., 1977).
There are three important regimes in which the hy-
perfine interaction leads to spin dephasing of localized
electrons:
(i) In the limit of small orbital and spin correla-
tion between separated electron states and nuclear spin
states, spatial variations in Bn lead to inhomogeneous
dephasing of the spin ensemble, with the rate propor-
tional to the r.m.s. of Bn, given by the correspond-
ing thermal or nonequilibrium distribution of the nuclear
spins. Such inhomogeneous dephasing is seen by electron
spin resonance (ESR) experiments on donor states both
in Si (Feher and Gere, 1959) and in GaAs (Seck et al.,
1997). This effect can be removed by spin echo exper-
iments (in Si donor states performed, for example, by
Gordon and Browers (1958)). The spread in the Lar-
mor precession period due to the variance in Bn in GaAs
is estimated to be around 1 ns (Dzhioev et al., 2002b;
Merkulov et al., 2002)).
(ii) Temporal fluctuations in Bn, which can occur due
to nuclear dipole-dipole interactions, lead to irreversible
spin dephasing and decoherence of electron spins. Such
processes are sometimes referred to as spectral diffusion,
since the electron Zeeman levels split by Bn undergo ran-
dom shifts (de Sousa and Das Sarma, 2003c). The typi-
cal time scale for the fluctuations in GaAs is given by the
nuclear Larmor precession period in the field of neighbor-
ing nuclei and is of order 100 µs (Merkulov et al., 2002).
Nuclear moments also precess (and orient) in the mag-
netic fields of polarized electrons, an effect important
in optical orientation (Meier and Zakharchenya (Eds.),
1984), where the feedback from this precession can be
directly observed through the modulated precession of
electron spins. The time scale for the Larmor preces-
sion of nuclear spins in hyperfine fields is 1 µs in GaAs
(Merkulov et al., 2002), so this effect does not lead to
motional narrowing of Bn; electron spins precess many
times before the nuclear spin flips.
(iii) In the presence of strong orbital correlations (elec-
tron hopping or recombination with acceptor hole states)
or spin (direct exchange interaction) between neighboring
electron states, spin precession due to Bn is motionally
narrowed. While the direct spin exchange interaction
does not cause ensemble spin relaxation (the total spin
is preserved in spin flip-flops), it leads to individual spin
decoherence, which can be much faster than what is in-
ferred from T2. This effect is much more pronounced
in GaAs than in Si, since the donor states spread to
greater distances, and thus even in the low-doping lim-
its (≈ 1014 cm−3 donors) the exchange interaction can

39
performed by Fabian and Das Sarma (1999b) and com-
pared to the experimental data available for T < 100
K (Johnson and Silsbee, 1985, 1988d). Figure 16 shows
both the experiment and the theory. In the experimen-
tal data only the phonon contribution to 1/τs is re-
tained (Johnson and Silsbee, 1985); the constant back-
ground impurity scattering is removed. The figure shows
a rapid decrease of τs with increasing T at low T , where
the agreement between experiment and theory is very
good. Above 200 K (the Debye temperature TD ≈ 400
K) the calculation predicts a linear dependence τs[ns] ≈
24 × T−1[K−1]. In the phonon-dominated linear regime
the EY mechanism predicts that the ratio aph = τp/τs
does not depend on T (see Sec. III.B.1). The calcu-
lated value is aphth = 1.2× 10−4 (Fabian and Das Sarma,
1999b), showing that 104 phonon scatterings are needed
to randomize electron spin.
An important step towards extending spin injec-
tion capabilities was undertaken recently by achieving
spin injection into Cu and Al at room temperature
(Jedema et al., 2002a, 2001, 2002b, 2003); the measured
data are unique in providing reliable values for spin dif-
fusion lengths and spin relaxation times in these two
important metals at room temperature. The measured
values for Al are somewhat sensitive to the experimen-
tal procedure/data analysis: τs = 85 ps (Jedema et al.,
2002b) and τs = 124 ps (Jedema et al., 2003), as com-
pared to τs = 90 ps predicted by the theory at T = 293
K. The room temperature experimental data are in-
cluded in Fig. 16 for comparison. They nicely con-
firm the theoretical prediction. Less sensitive to data
analysis is the ratio aph, for which the experiments
give 1.1 × 10−4 (Jedema et al., 2002b) and 1.3 × 10−4
(Jedema et al., 2003), comparing favorably with the the-
oretical aphth = 1.2× 10−4.
Spin relaxation in Al depends rather strongly on
magnetic fields at low T . CESR measurements
(Lubzens and Schultz, 1976a,b) show that at tempera-
tures below 100 K, 1/τs increases linearly with increas-
ing B. A specific sample (Lubzens and Schultz, 1976b)
showed a decrease of τs from about 20 ns to 1 ns, upon
increase in B from 0.05 to 1.4 T. It was proposed that the
observed behavior was due to cyclotron motion through
spin hot spots (Silsbee and Beuneu, 1983). The reason-
ing is as follows. Assume that there is considerable spread
(anisotropy) δg ≈ ∆g of the g factors over the Fermi sur-
face. Such a situation is common in polyvalent metals,
whose spin hot spots have anomalously large spin-orbit
coupling. In a magnetic field the electron spins precess
correspondingly with rates varying by δΩL ≈ (δg/g)ΩL,
where ΩL is the Larmor frequency. Motional narrow-
ing leads to 1/τs ≈ (δΩL)2τc, where τc is the correlation
time for the random changes in g. At small magnetic
fields τc = τp and 1/τs ∼ B2τp. Such a quadratic de-
pendence of 1/τs on B is a typical motional narrowing
case and has been observed at low temperatures in Cu
(Lubzens and Schultz, 1976b). As the field increases τc
becomes the time of flight through spin hot spots, in
0 100 200 300 400 500
T (K)
10-2
100
102
104
T 1

(ns
)
Johnson & Silsbee
Lubzens & Schultz
Fabian & Das Sarma
293 K: Jedema et al.
FIG. 16 Measured and calculated τs in Al. The low-T
measurements are CESR (Lubzens and Schultz, 1976b) and
spin injection (Johnson and Silsbee, 1985). Only the phonon
contribution is shown, as adapted from Johnson and Silsbee
(1985). The solid line is the first-principles calculation, not a
fit to the data, (Fabian and Das Sarma, 1998). The data at
T = 293 K are results from room-temperature spin injection
experiments of Jedema et al. (2002b, 2003). Adapted from
Fabian and Das Sarma, 1999b.
which case τc ∼ 1/B. As a result 1/τs acquires a compo-
nent linear in B, in accord with experiment.
In an effort to directly detect phonon-induced spin
flips in Al, an interesting experiment was devised
(Grimaldi and Fulde, 1996; Lang et al., 1996) using the
Zeeman splitting of the energy gap in Al superconduct-
ing tunnel junctions. Although the experiment failed,
due to overwhelming spin-flip boundary scattering, it
showed the direction for future research in studying spin-
flip electron-phonon interactions.
D. Spin relaxation in semiconductors
Although sorting out different spin-relaxation mecha-
nisms of conduction electrons in semiconductors is a dif-
ficult task, it has generally been observed that the EY
mechanism is relevant in small-gap and large-spin-orbit
coupling semiconductors, while the DP processes are re-
sponsible for spin dephasing in middle-gap materials and
at high temperatures. In heavily p-doped samples the
BAP mechanism dominates at lower temperatures, while
DP at higher. In low-doped systems the DP dominates
over the whole temperature range where electron states
are extended. Spin relaxation of bound electrons pro-
ceeds through the hyperfine interaction. Finally, spin
relaxation of holes is due to the EY processes. In bulk
III-V or II-VI materials, for holes τs ≈ τp, since the va-
lence spin and orbital states are completely mixed. How-
ever, in two-dimensional systems, where the heavy and
light hole states are split, hole spin relaxation is much
less effective.

41
temperature CESR linewidth is about 8 G, corresponding
to the electron spin lifetime of 7 ns.
2. Low-dimensional semiconductor structures
The importance of low-dimensional semiconductor sys-
tems (quantum wells, wires, and dots) lies in their great
flexibility in manipulating charge and, now, also spin
properties of the electronic states. Studies of spin relax-
ation in those systems are driven not only by the need for
fundamental understanding of spin relaxation and deco-
herence, but also by the goal of finding ways to reduce or
otherwise control spin relaxation and coherence in gen-
eral. For a survey of spin relaxation properties of semi-
conductor quantum wells, see Sham (1993).
Spin relaxation in semiconductor heterostructures is
caused by random magnetic fields originating either from
the base material or from the heterostructure itself. All
four mechanisms of spin relaxation can be important,
depending on the material, doping, and geometry. The
difference from the bulk is the localization of the wave
function into two, one, or zero dimensions and the ap-
pearance of structure-induced random magnetic fields.
Of all the mechanisms, the DP and HFI are believed to
be most relevant.
The most studied systems are GaAs/AlGaAs QW’s.
The observed τs varies from nanoseconds to picoseconds,
depending on the range of control parameters such as
temperature, QW width or confinement energy E1, car-
rier concentration, mobility, magnetic field, or bias.84
Spin relaxation has also been investigated in
In/GaAs (Cortez et al., 2002; Paillard et al., 2001), in
an InAs/GaSb superlattice (Olesberg et al., 2001), in In-
GaAs (Guettler et al., 1998), in GaAsSb multiple QW’s
by (Hall et al., 1999). II-VI QW’s (specifically ZnCdSe)
were studied by Kikkawa et al. (1997), finding τs ≈ 1 ns,
weakly dependent on both mobility and temperature (in
the range 5 < T < 270 K). Electron and hole spin dephas-
ing have also been investigated in dilute magnetic semi-
conductor QW’s doped with Mn ions (Camilleri et al.,
2001; Crooker et al., 1997).
Reduction of spin relaxation by inhibiting the BAP
electron-hole exchange interaction through spatially sep-
arating the two carriers has been demonstrated in δ-
doped p-GaAs:Be/AlGaAs (Wagner et al., 1993). The
84 Here is a list of selected references with useful data on
τs in GaAs/AlGaAs QW’s: confinement energy depen-
dence has been studied by Britton et al. (1998); Endo et al.
(2000); Malinowski et al. (2000); Ohno et al. (2000c, 1999a);
Tackeuchi et al. (1996); temperature dependence is treated
by Adachi et al. (2001); Malinowski et al. (2000); Ohno et al.
(2000c, 1999a); Wagner et al. (1993); carrier concentration de-
pendence is studied by Sandhu et al. (2001); dependence on mo-
bility is examined by Ohno et al. (1999a); and dependence on
magnetic field in studied by Zhitomirskii et al. (1993).
observed τs was ≈ 20 ns at T < 10 K, which is in-
deed unusually large. The exchange interaction was also
studied at room temperature, observing an increase of
τs with bias voltage which increases spatial separation
between electrons and holes, reducing the BAP effects
(Gotoh et al., 2000). In the fractional quantum Hall ef-
fect regime it was demonstrated (Kuzma et al., 1998)
that nonequilibrium spin polarization in GaAs QW’s can
survive for tens of µs. Spin lifetime was also found to
be enhanced in GaAs QW’s strained by surface acous-
tic waves (Sogawa et al., 2001). A theoretical study
(Kiselev and Kim, 2000) proposed that spin dephasing
in 2DEG can be significantly suppressed by constraining
the system to finite stripes, several mean free paths wide.
Theoretical studies focusing on spin dephasing in
III-V and II-VI systems include those of (Bronold et al.,
2002; Krishnamurthy et al., 2003; Lau and Flatte´,
2002; Lau et al., 2001; Puller et al., 2003; Wu, 2001;
Wu and Kuwata-Gonokami, 2002; Wu and Metiu, 2000).
Spin relaxation due to the DP mechanism with bulk
inversion asymmetry term in the important case of
GaAs/AlGaAs rectangular QW’s was investigated by
Monte-Carlo simulations (Bournel et al., 2000) at room
temperature, including interface roughness scattering.
Nice agreement with experiment was found for τs(E1),
where E1 is the confinement energy. Interface rough-
ness becomes important at large values of E1, where
scattering increases τs (see also Sherman (2003b)).
Spin relaxation and spin coherence of spin-polarized
photoexcited electrons and holes in symmetric p- and n-
doped and undoped GaAs/AlGaAs quantum wells was
investigated using rate equations (Uenoyama and Sham,
1990a,b). It was shown that in these heterostructures
hole spin relaxation proceeds slower than electron-hole
recombination. Hole relaxation is found to occur mostly
due to acoustic phonon emission. The ratio of the spin-
conserving to spin-flip hole relaxation times was found
to be 0.46, consistent with the fact that luminescence
is polarized even in n-doped quantum wells at times
greater than the momentum relaxation time. Similar
observations hold for strained bulk GaAs, where hole
spin relaxation is also reduced. Spin relaxation of holes
in quantum wells was calculated (Bastard and Ferreira,
1992; Ferreira and Bastard, 1991) using the interaction
with ionized impurities and s-d exchange in semimagnetic
semiconductors. It was shown that size quantization sig-
nificantly reduces spin relaxation of holes, due to the lift-
ing of heavy and light hole degeneracy. The observed spin
lifetimes for holes at low temperatures reached up to 1
ns, while at T > 50 K in the same samples τs got smaller
than 5 ps (Baylac et al., 1995).
Spin dynamics and spin relaxation of excitons in
GaAs (Munoz et al., 1995; Vina et al., 2001) and ZnSe
(Kalt et al., 2000) were investigated experimentally and
theoretically (Maialle et al., 1993; Sham et al., 1998).
Coherent spin dynamics in magnetic semiconductors was
considered by Linder and Sham (1998).
Spin relaxation in Si heterostructures has been in-

44
0 50 100 150 200
temperature (K)
102
103
104
105
106
T* 2
(p
s)
B=0
B=4 T
FIG. 19 Measured temperature dependence of the spin de-
phasing time for bulk n-GaAs doped with Nd = 1×1016 cm−3
Si donors, at B = 0 and B = 4 T. The sample is insulating at
low T and nondegenerate at high T (T >∼ 50 K, assuming ≈ 4
meV for the donor binding energy), where donors are ionized.
Adapted from Kikkawa and Awschalom, 1998.
the zero-field data the initial decrease of τs with B is
very rapid, dropping from 130 ns at 5 K to less than
1 ns at 150 K. However, the sample held at B = 4 T
shows at first a rapid increase with increasing T , and
then a decrease at T ≈ 50 K. The decrease of τs with
increasing T above 50 K has been found to be consis-
tent with the DP mechanism (Kikkawa and Awschalom,
1998), taking τs ∼ T−3 in Eq. (74), while extracting the
temperature dependence of τp from the measurement of
mobility. The DP mechanism for conduction electrons
was also observed in p-GaAs in the regime of nondegen-
erate hole densities Na ≈ 1017 cm−3 at temperatures
above 100 K (Aronov et al., 1983), after the contribu-
tion from the BAP mechanism was subtracted using a
theoretical prediction. From the observed mobility it was
found that τp(T ) ∼ T−0.8, so that according to the DP
mechanism τs ∼ T−2.2, which is indeed consistent with
the experimental data. The origin of τs(T ) below 50 K
in Fig. 19 is less obvious. At low T , electrons are lo-
calized, so in order to explain the experimental data the
theory should include ionization of donors. The increase
with increasing T of τs at 4 T invokes a picture of mo-
tional narrowing in which the correlation time decreases
with increasing T much faster than the dispersion of lo-
cal Larmor frequencies. We do not know of a satisfactory
quantitative explanation for these experimental results.87
87 There is a discrepancy in the data presented in Figs. 18 and 19.
Take the Nd = 1×1016 cm−3 sample. While Fig. 18 reports τs ≈
3 ns at 5 K and 4 T, τs is only about 1 ns in Fig. 19. The reason
for this difference (Kikkawa, 2003) turns out to be electronically-
induced nuclear polarization (Kikkawa and Awschalom, 2000).
At low temperatures and large magnetic fields, nuclear po-
larization develops via the Overhauser effect inhomogeneously
Similar behavior of τs(T ) in insulating samples was found
in GaN (Beschoten et al., 2001).
The temperature dependence of τs for samples with
Nd ≫ Ndc has been reported (Kikkawa and Awschalom,
1998) to be very weak, indicating, for these degenerate
electron densities, that τp(T ) is only weakly dependent
on T . What can be expected for τs at room temperature?
The answer will certainly depend on Nd. Recent ex-
periments on time- resolved Kerr rotation (Kimel et al.,
2001) suggest that 5 ps< τs < 10 ps for undoped GaAs
and 15 ps < τs < 35 ps for a heavily doped n-GaAs with
Nd = 2× 1018 cm−3.
For spintronic applications to make use of the large
τs observed in bulk n-GaAs one is limited to both very
small temperatures and small doping levels. Although
this may restrict the design of room-temperature spin-
tronic devices, such a regime seems acceptable for spin-
based quantum computing (see Sec. IV.F), where one is
interested in the spin lifetime of single (or a few) elec-
trons, bound to impurities or confined to quantum dots.
How close is τs to the individual spin lifetime τsc? There
is no clear answer yet. Ensemble spin dephasing seen for
insulating GaAs samples appears to be due to motional
narrowing of the hyperfine interaction. The randomizing
processes are spin flips due to the direct exchange, lead-
ing to the correlation time τc, which can be taken as a
measure for the lifetime τsc of the individual spins. Ex-
tracting this lifetime from the experiment is not easy, but
the obvious trend is the smaller the τc, the larger the τs.
For a specific model of spin relaxation in bound electron
states τc was extracted experimentally by Dzhioev et al.
(2002c) by detecting the changes in the spin polarization
due to longitudinal magnetic fields. The result is shown
in Fig. 17. The two times, τc and τs differ by orders of
magnitude. For the doping levels where τs is greater than
100 ns, τc is smaller than 0.1 ns. Unfortunately, the use-
ful time for spin quantum computing would be extracted
in the limit of very small dopings, where the data are still
sparse. For an informal recent review of τs in n-GaAs,
see Kavokin (2002a).
Closely related to spin relaxation is spin diffusion.
Ha¨gele et al. (1998) observed the transport of a spin
population—longitudinal spin drift—in i-GaAs over a
throughout the electron spin excitation region. The inhomoge-
neous magnetic field due to polarized nuclei causes inhomoge-
neous broadening of the electronic τs. The measured spin de-
phasing time is indeed T ∗2 , rather than the intrinsic T2. Further-
more, since nuclear polarization typically takes minutes to de-
velop, the measured T ∗2 depends on the measurement “history.”
This is the reason why two different measurements, reported in
Figs. 18 and 19, show different T ∗2 under otherwise equivalent
conditions. The nuclear polarization effect is also part of the
reason why the T2(T ) at 4 T sharply deviates from that at zero
field at small T . The technique should give consistent results at
small fields and large temperatures, as well as in heavily doped
samples where the nuclear fields are motionally narrowed by the
itinerant nature of electrons.

45
length scale greater than 4 µm in electric fields up to
6 kV/cm and at low temperatures. This was followed by
a remarkable result of Kikkawa and Awschalom (1999),
the observation of the drift of precessing electron spins—
transverse spin drift—in GaAs with Nd = 1×1016 cm−3,
over 100 µm in moderate electric fields (tens of V/cm)
at T = 1.6 K, setting the length scale for the spin de-
phasing. By directly analyzing the spreading and drift-
ing of the electron spin packets in time, Kikkawa and
Awschalom obtained the spin diffusion (responsible for
spreading) and electronic diffusion (drift by electric field)
coefficients. It was found that the former is about 20
times as large as the latter. These results are difficult
to interpret, since the sample is just below the metal-
to-insulator transition, where charge is transported via
hopping, but they suggest that spin diffusion is strongly
enhanced through the exchange interaction. Investiga-
tions of this type in even smaller doping limits may prove
important for understanding single-spin coherence.
b. GaAs-based quantum wells. We discuss selected exper-
imental results on spin relaxation in GaAs/AlxGa1−xAs
QW’s, presenting the temperature and confinement en-
ergy dependence of τs.
Figure 20 plots the temperature dependence of 1/τs in
the interval of 90 < T < 300 K for QW’s of width L
ranging from 6 to 20 nm (Malinowski et al., 2000). The
wells, with x = 0.35 and orientation along [001], were
grown on a single wafer to minimize sample-to-sample
variations when comparing different wells. The reported
interface roughness was less than the exciton Bohr radius
of 13 nm. In these structures the excitonic effects domi-
nate at T < 50 K (with the reported τs ≈ 50 ps), while
the exciton ionization is complete roughly at T > 90 K,
so the data presented are for free electrons. Spin relax-
ation was studied using pump-probe optical orientation
spectroscopy with a 2 ps time resolution and the typical
excitation intensity/pulse of 1010 cm−2.
As Fig. 20 shows, τs depends rather weakly on T for the
narrow wells with L < 10 nm. For the well with L = 15
nm, after being approximately constant (or somewhat
decreasing) as T increases to about 200 K, τs increases
with increasing T at greater temperatures. The increase
is consistent with the 1/τs ∼ T 2 behavior. The thick-
est well increases with the same power law, 1/τs ∼ T 2,
over the whole temperature range. In order to make a
reliable comparison with theoretical predictions (the ex-
pected mechanism is that of DP in two-dimensional sys-
tems), one needs to know the behavior of τp(T ). The
DP mechanism predicts, for the nondegenerate electron
densities employed in the experiment, that 1/τs ∼ T 3τp
[see Eq. (74)] in the bulk and wide QD’s, the condition
being that thermal energy is greater than the subband
separation), and 1/τs ∼ TE21τp from Eq. (79) for the
bulk inversion asymmetry after making thermal averag-
ing (Ek → kBT ), when one realizes that confinement
energy E1 is ∼ 〈k2n〉. When one assumes that momen-
Temperature (K)
80 150 200 250 300100
S
pi
n
re
la
xa
tio
n
ra
te
(p
s-
1 )
0.0001
0.001
0.01
0.1
bulk GaAs
~T2
6 nm
10 nm
15 nm
20 nm
FIG. 20 Measured temperature dependence of the
conduction-electron-spin relaxation rate 1/τs in
GaAs/AlGaAs QW’s of varying widths: the dashed
curve, data for a low-doped (Na = 4 × 1016 cm−3) bulk
p-GaAs (Meier and Zakharchenya (Eds.), 1984); solid line,
the τs ∼ T 2 dependence. From Malinowski et al., 2000.
tum relaxation in these elevated temperatures is due to
scattering by phonons, τp should be similar in bulk and
low-dimensional structures. From the observed high-
temperature bulk τs(T ) (at low temperatures τs is af-
fected by BAP processes) one can estimate τp ∼ 1/T ,
which is consistent with the constant τs for the narrow
wells, and with the quadratic dependence for the wide
wells. At low T , in addition to the BAP mechanism, τs
will deviate from that in the bulk due to impurity scat-
tering. The EY and BAP mechanisms were found not
to be relevant to the observed data (Malinowski et al.,
2000).
Figure 21 shows the dependence of 1/τs on the ex-
perimentally determined confinement energy E1 for a
variety of QW’s on the same wafer (Malinowski et al.,
2000). The data are at room temperature. The spin
relaxation time varies from somewhat less than 100
ps for wide QW’s, approximating the bulk data (cf.
Kimel et al. (2001) where 15 ps < τs < 35 ps was
found for a heavily doped n-GaAs), to about 10 ps in
most confined structures. The downturn for the highest-
E1 well (of width 3 nm) is most likely due to the in-
creased importance of interface roughness at such small
widths (Malinowski et al., 2000). Confinement strongly
enhances spin relaxation. This is consistent with the
DP mechanism for two-dimensional systems, in which
the spin precession about the intrinsic magnetic fields
(here induced by bulk inversion asymmetry) increases as
E21 with increasing confinement. The observed data in
Fig. 21 are consistent with the theoretical prediction.
Similarly to bulk GaAs, spin relaxation in GaAs QW’s

46
E1e (meV)
0 20 40 60 80 100 120 140
S
pi
n
R
el
ax
at
io
n
R
at
e
(p
s-
1 )
0.00
0.02
0.04
0.06
0.08
0.10
FIG. 21 Measured room-temperature dependence of 1/τs on
the confinement energy E1 for GaAs/AlGaAs QW’s. The
solid line is a quadratic fit, showing behavior consistent with
the DP mechanism. From Malinowski et al., 2000.
was found to be reduced at carrier concentrations close
to the metal-to-insulator transition (n ≈ 5× 1010 cm−2)
(Sandhu et al., 2001).
IV. SPINTRONIC DEVICES AND APPLICATIONS
In this section we focus primarily on the physical prin-
ciples and materials issues for various device schemes,
which, while not yet commercially viable, are likely to
influence future spintronic research and possible applica-
tions.
A. Spin-polarized transport
1. F/I/S tunneling
Experiments reviewed by Tedrow and Meservey (1994)
in ferromagnet/insulator/superconductor (F/I/S) junc-
tions have established a sensitive technique for measur-
ing the spin polarization P of magnetic thin films and,
at the same time, has demonstrated that the current will
remain spin-polarized after tunneling through an insu-
lator. These experiments also stimulated more recent
imaging techniques based on the spin-polarized STM (see
Johnson and Clarke (1990); Wiesendanger et al. (1990);
and a review, Wiesendanger (1998)) with the ultimate
goal of imaging spin configurations down to the atomic
level.
The degree of spin polarization is important for many
applications such as determining the magnitude of tun-
neling magnetoresistance (TMR) in magnetic tunnel
junctions (MTJ) [recall Eq. (2)]. Different probes for
spin polarization generally can measure significantly dif-
ferent values even in experiments performed on the same
homogeneous sample. In an actual MTJ, measured po-
larization is not an intrinsic property of the F region and
could depend on interfacial properties and the choice of
insulating barrier. Challenges in quantifying P , discussed
here in the context of F/I/S tunneling, even when F is
a simple ferromagnetic metal, should serve as a caution
for studies of novel, more exotic, spintronic materials.
F/I/S tunneling conductance is shown in Fig. 22,
where for simplicity we assume that the spin-
orbit and spin-flip scattering (see Sec. III.C) can
be neglected, a good approximation for Al2O3/Al
(Tedrow and Meservey, 1971a, 1994), a common choice
for I/S regions. For each spin the normalized BCS density
of states is N˜S(E) = Re(|E|/2
√
E2 −∆2), where E is the
quasiparticle excitation energy and ∆ the superconduct-
ing gap.88 The BCS density of states is split in a mag-
netic field H, applied parallel to the interface, due to a
shift in quasiparticle energy E → E±µBH , for ↑ (↓) spin
parallel (antiparallel) to the field, where µB is the Bohr
magneton. The tunneling conductance is normalized
with respect to its normal state value–for an F/I/N junc-
tion, G(V ) ≡ (dI/dV )S/(dI/dV )N = G↑(V ) + G↓(V ),
where V is the applied bias. This conductance can be ex-
pressed by generalizing analysis of Giaever and Megerle
(1961) as
G(V ) =
∫ ∞
−∞
1 + P
2
N˜S(E + µH)βdE
4 cosh2[β(E + qV )/2]
(99)
+
∫ ∞
−∞
1− P
2
N˜S(E − µH)βdE
4 cosh2[β(E + qV )/2]
.
Here β = 1/kBT , kB is the Boltzmann constant, T
is the temperature, and q is the proton charge. The
factors (1 ± P )/2 represent the difference in tunneling
probability between for ↑ and ↓ electrons. While a rig-
orous determination of P , in terms of materials parame-
ters, would require a full calculation of spin-dependent
tunneling, including the appropriate boundary condi-
tions and a detailed understanding of the interface prop-
erties, it is customary to make some simplifications.
Usually P can be identified as (Maekawa et al., 2002;
Worledge and Geballe, 2000a)
P → PG = (GN↑ −GN↓)/(GN↑ +GN↓), (100)
the spin polarization of the normal-state conductance
(proportional to the weighted average of the density of
states in F and S and the square of the tunneling ma-
trix element), where ↑ is the electron spin with the
magnetic moment parallel to the applied field (major-
ity electrons in F). With the further simplification of
88 Here we focus on a conventional s-wave superconductor with no
angular dependence in ∆.

47
0 qV/∆
(a) N ,
1−1
µ /2 HB ∆
0 qV/∆
(b) G ,
1−1
FIG. 22 Ferromagnet/insulator/superconductor tunneling in
an applied magnetic filed: (a) Zeeman splitting of the BCS
density of states as a function of applied bias; (b) normal-
ized spin-resolved conductance (dashed lines) and the total
conductance (solid line) at finite temperature.
spin-independent and constant tunneling matrix element
(Tedrow and Meservey, 1971b, 1994), Eq. (100) can be
expressed as
P → PN = (NF↑ −NF↓)/(NF↑ +NF↓), (101)
the spin polarization of the tunneling density of states in
the F region at the Fermi level.
Spin polarization P of the F electrode can be deduced
(Tedrow and Meservey, 1994) from the asymmetry of the
conductance amplitudes at the four peaks in Fig. 22 (b)
[for P=0, G(V)=G(-V)]. In CrO2/I/S tunnel junctions,
nearly complete spin polarization PG > 0.9 was measured
(Parker et al., 2002). Only two of the four peaks sketched
in Fig. 22, have been observed, indicating no features
due to the minority spin up to H=2.5 T. Parkin et al.
(2004) have shown that by replacing an aluminum oxide
(a typical choice for an insulating region) with magne-
sium oxide, one can significantly increase the spin polar-
ization in F/I/S junctions. Correspondingly, extraordi-
narily large values of TMR (> 200% at room tempera-
ture) can be achieved even with conventional ferromag-
netic CoFe) electrodes.
The assumption of spin-conserving tunneling
can be generalized (Monsma and Parkin, 2000a,b;
Tedrow and Meservey, 1994; Worledge and Geballe,
2000a) to extract P in the presence of spin-
orbit and spin-flip scattering. Theoretical analyses
(Bruno and Schwartz, 1973; Fulde, 1973; Maki, 1964)
using many-body techniques show that the spin-orbit
scattering would smear the Zeeman-split density of
states, eventually merging the four peaks into two,
while the magnetic impurities (Abrikosov and Gorkov,
1960) act as pair breakers and reduce the value of ∆.
Neglecting the spin-orbit scattering was shown to lead to
the extraction of higher P values (Monsma and Parkin,
2000a; Tedrow and Meservey, 1994).
With a few exceptions (Worledge and Geballe,
2000b), F/I/S conductance measurements
(Tedrow and Meservey, 1994) have revealed posi-
tive P–the dominant contribution of majority spin
electrons for different ferromagnetic films (for example,
in Fe, Ni, Co and Gd). However, electronic structure
calculations typically give that NF↑ < NF↓ and PN < 0
[for Ni and Co NF↑/NF↓ ∼ 1/10 (Butler et al., 2001)].
Early theoretical work addressed this apparent differ-
ence,89 and efforts to understand precisely what is being
experimentally measured have continued.
Stearns (1977) suggested that only itinerant, freelike
electrons will contribute to tunneling, while nearly lo-
calized electrons, with a large effective mass, contribute
to the total density of states but not to G(V) [see
also Hertz and Aoi (1973) and, for spin-unpolarized tun-
neling, Gadzuk (1969)]. From the assumed parabolic
dispersion of the spin subbands with fixed spin split-
ting, Stearns related the measured polarization to the
magnetic moment, giving positive P → Pk = (kF↑ −
kF↓)/(kF↑ + kF↓), the spin polarization of the projec-
tions of Fermi wave vectors perpendicular to the in-
terface. Similar arguments, for inequivalent density-of-
states contributions to G(V), were generalized to more
complex electronic structure. Mazin (1999) showed the
importance of the tunneling matrix elements which have
different Fermi velocities for different bands [see also
(Yusof et al., 1998), in the context of tunneling in a high
temperature superconductor (HTSC)]. Consequently, PG
could even have an opposite sign from PN –which, for ex-
ample, would be measured by spin-resolved photoemis-
sion.
Good agreement between tunneling data and electronic
structure calculations was illustrated by the example
of NixFe1−x (Nadgorny et al., 2000), showing, however,
that P is not directly related to the magnetic moment
(Meservey et al., 1976). The difference between bulk and
the surface densities of states of the ferromagnet (probed
in tunneling measurements) (Oleinik et al., 2000), the
choice of tunneling barrier (De Teresa et al., 1999), and
details of the interfacial properties, which can change
over time (Monsma and Parkin, 2000b), have all been
shown to affect the measured P directly.
Tedrow-Meservey technique is also considered as a
probe to detect spin injection in Si, where optical meth-
ods, due to the indirect gap, would be ineffective. F/I/S
tunneling was also studied using amorphous Si (a-Si)
and Ge (a-Ge) as a barrier. While with a-Si some
spin polarization was detected (Meservey et al., 1982) no
spin-polarized tunneling was observed using a-Ge barrier
(Gibson and Meservey, 1985), in contrast to the first re-
ports of TMR (Julliere`, 1975).
Spin-dependent tunneling was also studied using a
HTSC electrode as a detector of spin polarization
(Chen et al., 2001; Vas’ko et al., 1998). While this can
significantly extend the temperature range in the tun-
neling experiments, a lack of understanding of HTSC’s
makes such structures more a test ground for funda-
mental physics than a quantitative tool for quantita-
tively determining P . There are also several important
differences between studies using HTSC’s and conven-
tional low-temperature superconductors. The supercon-
89 For a list of references see Tedrow and Meservey (1973, 1994).

49
can be expressed as in Eq. (2) but with the redefined
polarization
P → Pk(κ2 − kF↑kF↓)/(κ2 + kF↑kF↓), (102)
where Pk, as defined by Stearns (1977), is also PN (in
a free-electron picture) and iκ is the usual imaginary
wave vector through a square barrier. Through the de-
pendence of κ on V the resulting polarization in Slon-
czewski’s model can change sign. A study of a similar
geometry using a Boltzmann-like approach shows (Chui,
1997) that the spin splitting of electrochemical poten-
tials persists in the F region all the way to the F/I in-
terface, implying κ↑ 6= κ↓ and an additional voltage de-
pendence of the TMR. Variation of the density of states
[inferred from the spin-resolved photoemission data
(Park et al., 1998a,b)] within the range of applied bias in
MTJ’s of Co/SrTiO3/La0.7Sr0.3MnO3 (Co/STO/LSMO)
(De Teresa et al., 1999), together with Jullie`re’s model,
was used to explain the large negative TMR (-50% at 5
K), which would even change sign for positive bias (rais-
ing the Co Fermi level above the corresponding one of
LSMO). The bias dependence of the TMR was also at-
tributed to the density of states by extending the model
of a trapezoidal tunneling barrier (Brinkman et al., 1970)
to the spin-polarized case (Xiang et al., 2002).
The decay of TMR with temperature can be attributed
to several causes. Early theoretical work on N/I/N tun-
neling (Anderson, 1966; Appelbaum, 1966) [for a de-
tailed discussion and a review of related experimen-
tal results see Duke (1969)] showed that the presence
of magnetic impurities in the tunneling barrier pro-
duces temperature dependent conductance–referred to
as zero-bias anomalies. These findings, which consid-
ered both spin-dependent and spin-flip scattering, were
applied to fit the decay of the TMR with temperature
(Inoue and Makeawa, 1999; Jansen and Moodera, 2000;
Miyazaki, 2002). Hot electrons localized at F/I inter-
faces were predicted, to create magnons, or collective
spin excitations, near the F/I interfaces, and suppress
the TMR (Zhang et al., 1997). Magnons were observed
(Tsui et al., 1971) in an antiferromagnetic (AFM) NiO
barrier in single crystal Ni/NiO/Pb tunnel junctions and
were suggested (Moodera et al., 1995) as the cause of de-
creasing TMR with T by spin-flip scattering. Using an
s-d exchange (between itinerant s and nearly localized
d electrons) Hamiltonian, it was shown (Zhang et al.,
1997) that, at V → 0, G(T ) − G(0) ∝ T lnT , for
both ↑↑ and ↑↓ orientations. A different temperature
dependence of TMR was suggested by Moodera et al.
(1998). It was related to the decrease of the surface
magnetization (Pierce and Celotta, 1984; Pierce et al.,
1982) M(T )/M(0) ∝ T 3/2. Such a temperature depen-
dence [known as the Bloch’s law and reviewed by Krey
(2004)], attributed to magnons, was also obtained for
Sec. IV.A.3.
TMR (MacDonald et al., 1998). An additional decrease
of TMR with T was expected due to the spin-independent
part of G(T) (Shang et al., 1998), seen also in N/I/N
junctions.
Systematic studies of MTJ’s containing a semiconduc-
tor (Sm) region (used as a tunneling barrier and/or an
F electrode) have begun only recently.93 To improve
the performance of MTJ’s it is desirable to reduce the
junction resistance. A smaller RC constant would al-
low faster switching times in MRAM (for a detailed dis-
cussion see De Boeck et al. (2002)). Correspondingly,
using a semiconducting barrier could prove an alterna-
tive strategy for difficult fabrication of ultrathin (<1 nm
) oxide barriers (Rippard et al., 2002). Some F/Sm/F
MTJ’s have been grown epitaxially, and the amplitude
of TMR can be studied as function of the crystallo-
graphic orientation of a F/Sm interface. For an epitax-
ially grown Fe/ZnSe/Fe MTJ electronic structure cal-
culations have predicted (MacLaren et al., 1999) large
TMR (up to ∼1000 %), increasing with ZnSe thickness.
However, the observed TMR in Fe/ZnSe/Fe0.85Co0.15
was limited below 50 K, reaching 15 % at 10 K for
junctions of higher resistance and lower defect density94
(Gustavsson et al., 2001). Results on ZnS, another II-VI
semiconductor, demonstrated a TMR of ∼5 % at room
temperature (Guth et al., 2001).
There is also a possibility of using all-semiconductor
F/Sm/F single-crystalline MTJ’s where F is a ferromag-
netic semiconductor. These would simplify integration
with the existing conventional semiconductor-based elec-
tronics and allow flexibility of various doping profiles
and fabrication of quantum structures, as compared to
the conventional all-metal MTJ’s. Large TMR (>70
% at 8 K), shown in Fig. 23, has been measured in
an epitaxially grown (Ga,Mn)As/AlAs/(Ga,Mn)As junc-
tion (Tanaka and Higo, 2001). The results are consis-
tent with the k‖ being conserved in the tunneling pro-
cess (Mathon and Umerski, 1997), with the decrease of
TMR with T expected from the spin-wave excitations
(MacDonald et al., 1998; Shang et al., 1998), discussed
above. TMR is nonmonotonic with thickness in AlAs
(with the peak at ∼ 1.5 nm). For a given AlAs thick-
ness, double MTJ’s were also shown to give similar TMR
values and were used to determine electrically the spin in-
jection in GaAs QW (Mattana et al., 2003). However, a
room-temperature effect remains to be demonstrated as
the available well-characterized ferromagnetic semicon-
93 The early F/Ge/F results (Julliere`, 1975) were not reproduced
and other metallic structures involving Si, Ge, GaAs, and
GaN as a barrier have shown either no (Boeve et al., 2001;
Gibson and Meservey, 1985; Loraine et al., 2000) or only a small
(Jia et al., 1996; Kreuzer et al., 2002; Meservey et al., 1982)
spin-dependent signal.
94 Interface defects could diminish measured TMR. We recall (see
Sec. II.D.3) that at a ZnMnSe/AlGaAs interface they limit the
spin injection efficiency (Stroud et al., 2002) and from Eq. (32)
infer a reduced spin-valve effect.

51
and by matching the wave functions at the bound-
aries (interfaces) between different regions. Here Hλ is
the single-particle Hamiltonian for spin λ =↑, ↓ and λ
denotes a spin opposite to λ (de Jong and Beenakker,
1995; Zˇutic´ and Valls, 2000). ∆ is the pair potential
(de Gennes, 1989), E the excitation energy and uλ,
vλ are the electronlike quasiparticle and holelike quasi-
particle amplitudes, respectively.97 Griffin and Demers
(1971) have solved the Bogoliubov-de Gennes equations
with square or a δ-function barriers of varying strength
at an N/S interface. They obtained a result that in-
terpolates between the clean and the tunneling limits.
Blonder et al. (1982) used a similar approach, known
as the Blonder-Tinkham-Klapwijk method, in which the
two limits correspond to Z → 0 and Z → ∞, respec-
tively, and Z is the strength of the δ-function barrier.
The transparency of this approach98 makes it suitable
for the study of ballistic spin-polarized transport and
spin injection even in the absence of a superconducting
region (Heersche et al., 2001; Hu and Matsuyama, 2001;
Hu et al., 2001a; Matsuyama et al., 2002).
It is instructive to note a similarity between the two-
component transport in N/S junctions (for electronlike
and holelike quasiparticles) and F/N junctions (for spin
↑, ↓), which both lead to current conversion, accompanied
by the additional boundary resistance (Blonder et al.,
1982; van Son et al., 1987). In the N/S junction Andreev
reflection is responsible for the conversion between the
normal and the supercurrent, characterized by the su-
perconducting coherence length, while in the F/N case a
conversion between spin-polarized and unpolarized cur-
rent is characterized by the spin diffusion length.
For spin-polarized carriers, with different populations
in two spin subbands, only a fraction of the incident elec-
trons from a majority subband will have a minority sub-
band partner in order to be Andreev reflected. This can
be simply quantified at zero bias and Z = 0, in terms
of the total number of scattering channels (for each k‖)
Nλ = k2FλA/4π at the Fermi level. Here A is the point-
contact area, and kFλ is the spin-resolved Fermi wave
vector. A spherical Fermi surface in the F and S re-
gions, with no (spin-averaged) Fermi velocity mismatch,
is assumed. When S is in the normal state, the zero-
temperature Sharvin conductance is
GFN =
e2
h (N↑ +N↓), (104)
97 Equation (103) can be simply modified to include the spin flip
and spin-dependent interfacial scattering (Zˇutic´ and Das Sarma,
1999).
98 A good agreement (Yan et al., 2000) was obtained with the
more rigorous nonequilibrium Keldysh technique (Keldysh, 1964;
Rammer and Smith, 1986), for an illustration of how such a
technique can be used to study spin-polarized transport in a
wide range of heterojunctions see Me´lin and Feinberg (2002);
Zeng et al. (2003).
FIG. 24 The differential conductance for several spin-
polarized materials, showing the suppression of Andreev re-
flection with increasing PG. The vertical lines denote the
bulk superconducting gap for Nb: ∆(T = 0)=1.5 meV. Note
that NiMnSb, one of the Heusler alloys originally proposed
as half-metallic ferromagnets (de Groot et al., 1983b), shows
only partial spin polarization. From Soulen Jr. et al., 1998.
equivalent to R−1Sharvin, from Eq. (47). In the super-
conducting state all of the N↓ and only (N↓/N↑)N↑
scattering channels contribute to Andreev reflection
across the F/S interface and transfer charge 2e, yielding
(de Jong and Beenakker, 1995)
GFS =
e2
h
(
2N↓ +
2N↓
N↑
N↑
)
= 4
e2
h N↓. (105)
The suppression of the normalized zero-bias conductance
at V = 0 and Z = 0 (de Jong and Beenakker, 1995),
GFS/GFN = 2(1− PG) (106)
with the increase in the spin polarization PG → (N↑ −
N↓)/(N↑ + N↓), was used as a sensitive transport tech-
nique to detect spin polarization in a point contact
(Soulen Jr. et al., 1998). Data are given in Fig. 24. A
similar study, using a thin-film nanocontact geometry
(Upadhyay et al., 1998), emphasized the importance of
fitting the conductance data over a wide range of applied
bias, not only at V = 0, in order to extract the spin
polarization of the F region more precisely.
The advantage of such techniques is the detection
of polarization in a much wider range of materials
than those which can be grown for detection in F/I/S
or F/I/F tunnel junctions. A large number of ex-
perimental results using spin-polarized Andreev reflec-
tion has since been reported (Bourgeois et al., 2001;
Ji et al., 2001; Nadgorny et al., 2001; Panguluri et al.,
2003b; Parker et al., 2002), including the first direct mea-
surements (Braden et al., 2003; Panguluri et al., 2003a,
2004) of the spin polarization in (Ga,Mn)As and

52
(In,Mn)Sb.99 However, for a quantitative interpretation
of the measured polarization, important additional fac-
tors (similar to the limitations discussed for the appli-
cation of Jullie`re’s formula in Sec. IV.A.2) need to be
incorporated in the picture provided by Eq. (106). For
example, the Fermi surface may not be spherical [see
the discussion of Mazin (1999), specifying what type of
spin polarization is experimentally measured and also
that of Xia et al. (2002)]. The roughness or the size
of the F/S interface may lead to a diffusive compo-
nent of the transport (Fal’ko et al., 1999; Jedema et al.,
1999; Mazin et al., 2001). As a caution concerning the
possible difficulties in analyzing experimental data, we
mention some subtleties that arise even for the sim-
ple model of a spherical Fermi surface used to de-
scribe both F and S regions. Unlike charge trans-
port in N/S junctions (Blonder and Tinkham, 1983) in
a Griffin-Demers-Blonder-Tinkham-Klapwijk approach,
Fermi velocity mismatch between the F and the S re-
gions, does not simply increase the value of effective
Z. Specifically, at Z = V = 0 and normal incidence
it is possible to have perfect transparency even when
all the Fermi velocities differ, satisfying (vF↑vF↓)1/2 =
vS , where vS is the Fermi velocity in a superconduc-
tor (Zˇutic´ and Das Sarma, 1999; Zˇutic´ and Valls, 1999,
2000). In other words, unlike in Eq. (106), the spin polar-
ization (nonvanishing exchange energy) can increase the
subband conductance, for fixed Fermi velocity mismatch.
Conversely, at a fixed exchange energy, an increase in
Fermi velocity mismatch could increase the subgap con-
ductance.100 In a typical interpretation of a measured
conductance, complications can then arise in trying to
disentangle the influence of parameters Z, PG, and Fermi
velocity mismatch from the nature of the point contacts
(Kikuchi et al., 2002) and the role of inelastic scattering
(Auth et al., 2003). Detection of P in HTSC’s is even
possible with a large barrier or a vacuum between the F
and S regions, as proposed by Wang and Hu (2002) using
resonant Andreev reflection and a d-wave superconduc-
tor.101
Large magnetoresistive effects are predicted for crossed
Andreev reflection (Deutscher and Feinberg, 2000), when
the two F regions, separated within the distance of
99 Similar measurements were also suggested by
Zˇutic´ and Das Sarma (1999) to yield information about
the FSm/S interface. A more complete analysis should also
quantify the effects of spin-orbit coupling.
100 Similar results were also obtained when F and S region were sep-
arated with a quantum dot (Feng and Xiong, 2003; Zeng et al.,
2003; Zhu et al., 2002) and even in a 1D tight-binding model
with no spin polarization (Affleck et al., 2000).
101 Interference effects between the quasi-electron and quasi-hole
scattering trajectories that feel pair potentials of different sign
lead to a large conductance near zero bias, even at large in-
terfacial barrier (referred to as a zero-bias conductance peak in
Sec. IV.A.1).
the superconducting coherence length,102 are on the
same side of the S region. Such structures have also
been theoretically studied to understand the implica-
tions of nonlocal correlations (Apinyan and Me´lin, 2002;
Me´lin and Feinberg, 2002).
4. Spin-polarized drift and diffusion
Traditional semiconductor devices such as field-effect
transistors, bipolar diodes and transistors, or semicon-
ductor solar cells rely in great part on carriers (elec-
trons and holes) whose motion can be described as
drift and diffusion, limited by carrier recombination. In
inhomogeneous devices where charge buildup is rule,
the recombination-limited drift-diffusion is supplied by
Maxwell’s equations, to be solved in a self-consistent
manner. Many proposed spintronic devices as well as
experimental settings for spin injection (see Sec. II) can
be described by both carrier and spin drift and diffu-
sion, limited by carrier recombination and spin relax-
ation (Fabian et al., 2002b; Zˇutic´ et al., 2002). In addi-
tion, if spin precession is important for device operation,
spin dynamics need to be explicitly incorporated into the
transport equations (Qi and Zhang, 2003). Drift of the
spin-polarized carriers can be due not only to the elec-
tric field, but also to magnetic fields. We illustrate spin-
polarized drift and diffusion on the transport model of
spin-polarized bipolar transport, where bipolar refers to
the presence of electrons and holes, not spin up and down.
A spin-polarized unipolar transport can be obtained as
a limiting case by setting the electron-hole recombina-
tion rate to zero and considering only one type of carrier
(either electrons or holes).
Consider electrons and holes whose density is com-
monly denoted here as c (for carriers), moving in the
electrostatic potential φ which comprises both the exter-
nal bias V and the internal built-in fields due to charge
inhomogeneities. Let the equilibrium spin splitting of the
carrier band be 2qζc. The spin λ resolved carrier charge-
current density is (Zˇutic´ et al., 2002)
jcλ = −qµcλcλ∇φ±qDcλ∇cλ − qλµcλcλ∇ζc, (107)
where µ and D stand for mobility and diffusion coeffi-
cients, the upper sign is for electrons and the lower sign
is for holes. The first term on the right hand side de-
scribes drift caused by the total electric field, the sec-
ond term represents diffusion, while the last term stands
for magnetic drift—carrier drift in inhomogeneously split
bands.103 More transparent are the equations for the to-
102 Recent theoretical findings suggest that the separation should
not exceed the Fermi wavelength (Yamashita et al., 2003b).
103 Equation (107) can be viewed as the generalization of the Silsbee-
Johnson spin-charge coupling (Heide, 2001; Johnson and Silsbee,
1987; Wegrowe, 2000) to bipolar transport and to systems with
spatially inhomogeneous charge density.

54
FIG. 25 Photoinduced ferromagnetism in a (In,Mn)As/GaSb
heterostructure: (a) light-irradiated sample displaying pho-
toinduced ferromagnetism–direction of light irradiation is
shown by an arrow; (b) band-edge profile of (In,Mn)As/GaSb
heterostructure. Ec, conduction band, Ev, valence band; EF ,
Fermi level, respectively. From Koshihara et al., 1997.
For example, early work reporting ferromagnetism even
at nearly 900 K in La-doped CaBa6 (Ott et al., 2000;
Tromp et al., 2001; Young et al., 1999), was later revis-
ited suggesting extrinsic effect (Bennett et al., 2003). It
remains to be understood what the limitations are for
using extrinsic ferromagnets and, for example, whether
they can be effective spin injectors.
A high TC and almost complete spin polarization in
bulk samples are alone not sufficient for successful ap-
plications. Spintronic devices typically rely on inho-
mogeneous doping, structures of reduced dimensionality,
and/or structures containing different materials. Interfa-
cial properties, as discussed in the previous sections, can
significantly influence the magnitude of magnetoresistive
effects105 and the efficiency of spin injection. Doping
properties and possibility of fabricating a wide range of
structures allow spintronic applications beyond MR ef-
fects, for example, spin transistors, spin lasers, and spin-
based quantum computers (Sec. IV.F). Materials proper-
ties of hybrid F/Sm heterostructures, relevant to device
applications, were reviewed by Samarth et al. (2003).
Experiments in which the ferromagnetism is in-
duced optically (Koshihara et al., 1997; Oiwa et al.,
2002; Wang et al., 2003b) and electrically (Ohno et al.,
2000a; Park et al., 2002) provide a method for distin-
guishing the carrier-induced ferromagnetism, based on
the exchange interaction between the carrier and the
magnetic impurity spins, from ferromagnetism that origi-
nates from magnetic nanoclusters. Such experiments also
suggest a possible nonvolatile multifunctional devices
with tunable, optical, electrical, and magnetic properties.
105 In magnetic multilayers GMR is typically dominated by interfa-
cial scattering (Parkin, 1993), while in MTJ’s it is the surface
rather than the bulk electronic structure which influences the
relevant spin polarization.
FIG. 26 Magnetization curves for (In,Mn)As/GaSb at 5 K
observed before (open circles) and after (solid circles) light
irradiation. Solid line show a theoretical curve. (b) Hall re-
sistivity at 5 K before (dashed lines) and after (solid lines)
light irradiation. From Koshihara et al., 1997.
Comprehensive surveys of magneto-optical materials and
applications, not limited to semiconductors, are given by
Sugamo and Kojima (Eds.) (2000); Zvezdin and Kotov
(1997).
Photoinduced ferromagnetism was demonstrated by
Koshihara et al. (1997) in p-(In,Mn)As/GaSb het-
erostructure, shown in Figs. 25, and 26. Unpolarized
light penetrates through a thin (In,Mn)As layer and is
absorbed in the GaSb layer. A large band bending across
the heterostructures separates, by a built-in field, elec-
trons and holes. The excess holes generated in a GaSb
layer are effectively transferred to the p-doped (In,Mn)As
layer where they enhance the ferromagnetic spin ex-
change among Mn ions, resulting in a paramagnetic-
ferromagnetic transition.
The increase in magnetization, measured by a SQUID,
is shown in Fig. 26(a) and in Fig. 26(b) the corresponding
Hall resistivity
ρHall = R0B +RSM, (112)
is shown, where theR0 is the ordinary andRS the anoma-
lous Hall coefficient, respectively. Typical for (III,Mn)V
compounds, ρHall is dominated by the anomalous contri-
bution, ρHall ∝M .
A different type of photoinduced magnetization was

56
were measured–when VG is changed, the electron wave
function efficiently samples different regions with differ-
ent g factors (Salis et al., 2001b). Figure 28(a) gives
the time-resolved Kerr rotation data (the technique is
discussed in Sec. III) data which can be described as
∝ exp(−∆t/T ∗2 ) cos(Ω∆t), where ∆t is the delay time
between the circularly polarized pump and linearly po-
larized probe pulses, T∗2 is the transverse electron spin
lifetime with inhomogeneous broadening, and the angular
precession frequency Ω = µBgB/h¯ can be used to deter-
mine the g factor. It is also possible to manipulate g fac-
tors dynamically using time-dependent VG (Kato et al.,
2003). The anisotropy of g factor (g tensor) allows volt-
age control of both the magnitude and the direction of
the spin precession vector Ω.
C. Spin filters
Solid state spin filtering (recall the similarity with spin
injection from Sec II.C.1) was first realized in N/F/N
tunneling. It was shown by Esaki et al. (1967) that the
magnetic tunneling through (ferro)magnetic semiconduc-
tor Eu chalcogenides (Kasuya and Yanase, 1968; Nagaev,
1983; von Molna´r and Methfess, 1967), such as EuSe107
and EuS,108 could be modified by an applied magnetic
field. The change in I − V curves in the N/F/N struc-
ture, where N is a normal metal and F is a ferromagnet,
was explained by the influence of the magnetic field on
the height of the barrier formed at the N/F interface (for
EuSe, the barrier height was lowered by 25% at 2 T). The
large spin splitting of the Eu chalcogenides was subse-
quently employed in the absence of applied field with EuS
(Moodera et al., 1988) and nearly 100% spin polariza-
tion was reached at B=1.2 T with EuSe (Moodera et al.,
1993). These spin-filtering properties of the Eu chalco-
genides, used together with one-electron quantum dots,
were proposed as the basis for a method to convert sin-
gle spin into single charge measurements109 and provide
an important ingredient in realizing a quantum computer
(DiVincenzo, 1999), see Sec. IV.F.
Zeeman splitting in semiconductor heterostructures
and superlattices (enhanced by large g factors) (Egues,
1998; Guo et al., 2001), in quantum dots (Borda et al.,
2003; Deshmukh and Ralph, 2002; Recher et al., 2000),
and nanocrystals (Efros et al., 2001) provide effective
spin filtering and spin-polarized currents. Predicted
quantum size effects and resonance tunneling (Duke,
1969) also have their spin-dependent counterparts. The
structures studied are typically double-barrier resonant
107 At zero magnetic field EuSe is an antiferromagnet, and at mod-
erate fields it becomes a ferromagnet with TC≈ 5K.
108 At zero magnetic field, exchange splitting of a conduction band
in bulk EuS is ≈ 0.36 eV (Hao et al., 1990).
109 This method could already be realized using single-electron tran-
sistors or quantum point contacts.
FIG. 29 Mesoscopic spin filter: (a) micrograph and circuit
showing the polarizer-analyzer configuration used in the ex-
periment of Folk et al. (2003). The emitter (E) can be formed
into either a quantum dot or a quantum point contact (QPC).
The collector (C), is a single point contact. Electrons are fo-
cused from E to C through the base region (B), using a small
perpendicular magnetic field. Gates marked with “x” are left
undepleted when E is operated as a QPC; (b) base-collector
voltage (VC) showing two focusing peaks; (c) focusing peak
height at B‖=6 T with spin-selective collector QPC conduc-
tance (gC=0.5e2/h), comparing E as QPC at 2e2/h (dashed
curve) and E as a quantum dot with both leads at 2e2/h (solid
curve). Adapted from Folk et al., 2003.
tunneling diodes (for an early spin-unpolarized study see
Tsu and Esaki (1973)), with either Zeeman splitting or
using ferromagnetic materials, in which spin filtering can
be tuned by an applied bias.110
Several other realizations of spin filtering have been
investigated, relying on spin-orbit coupling.111 or hot-
electron transport across ferromagnetic regions,112 dis-
cussed in more detail in Sec. IV.E.3. A choice of particu-
110 See, for example, (Aleiner and Lyanda-Geller, 1991;
Brehmer et al., 1995; Giazotto et al., 2003; Mendez et al.,
1998; Ohno, 1998; Petukhov, 1998; Petukhov et al.,
2002; Slobodskyy et al., 2003; Ting and Cartoxia`, 2002;
Vurgaftman and Meyer, 2003).
111 These include the work of (de Andrada e Silva and La Rocca,
1999; Governale et al., 2002; Kiselev and Kim, 2001; Koga et al.,
2002b; Perel’ et al., 2003; Voskoboynikov et al., 1998, 1999).
112 See (Cacho et al., 2002; Filipe et al., 1998; Monsma et al.,
1995; Oberli et al., 1998; Rippard and Buhrman, 2000;
Upadhyay et al., 1999; van Dijken et al., 2002b).

58
spin
source
depletion
region
2qζ I
p n
V
Ip n
V
FIG. 30 Scheme of a magnetic bipolar diode. The p-region
(left) is magnetic, indicated by the spin splitting 2qζ of the
conduction band. The n-region (right) is nonmagnetic, but
spin polarized by a spin source: Filled circles, spin-polarized
electrons; empty circles, unpolarized holes. If the nonequi-
librium spin in the n-region is oriented parallel (top figure)
to the equilibrium spin in the p-region, large forward current
flows. If the relative orientation is antiparallel (bottom), the
current drops significantly. Adapted from Zˇutic´ et al., 2002.
proposed the magnetic bipolar diode described below.
The magnetic bipolar diode116 (MBD) is a p-n junction
diode with one or both regions magnetic (Fabian et al.,
2002b; Zˇutic´ et al., 2002). The MBD is the prototypical
device of bipolar spintronics, a subfield of spintronics in
which both electrons and holes take part in carrier trans-
port, while either electrons or holes (or both) are spin po-
larized (see Sec. IV.A.4). Examples of nonmagnetic bipo-
lar spintronic devices are the spin-polarized p-n junction
(Zˇutic´ et al., 2001b) and the spin solar cell (Zˇutic´ et al.,
2001a). These devices offer opportunities for effective
spin injection, spin amplification (see Sec. II.C.3), or spin
capacity—the effect of changing, by voltage, nonequilib-
rium spin density (Zˇutic´ et al., 2001b). The advantages
of magnetic bipolar spintronic devices (Fabian et al.,
2002a,b; Zˇutic´ et al., 2002, 2003) lie in the combina-
tion of equilibrium magnetism and nonequilibrium spin
and effective methods to manipulate a minority carrier
population. The most useful effects of the spin-charge
coupling in MBD’s are the spin-voltaic and the giant-
magnetoresistive effects, which are enhanced over those
of metallic systems by the exponential dependence of the
current on bias voltage.
A scheme of an MBD is shown in Fig. 30 (also see
Fig. 8). The p-region is magnetic, by which we mean
that it has a spin-split conduction band with the spin
splitting (Zeeman or exchange) 2qζ ∼ kBT . Zeeman
splitting can be significantly enhanced by the large g∗
factors of magnetically doped (Sec. II.C.3) or narrow-
116 Not to be confused with the usual magnetic diodes which are
ordinary diodes in a magnetic field. The I − V characteristics
of such diodes, depend on the magnetic field through small or-
bital effects on diffusion coefficient, not through the spin effects
described here.
band-gap semiconductors (Sec. IV.B). Using an MBD
with a ferromagnetic semiconductor slightly above its TC
is also expected to give large g∗ factors. The n-region is
nonmagnetic, but electrons can be spin-polarized by a
spin source (circularly polarized light or magnetic elec-
trode). The interplay between the equilibrium spin of
polarization Pn0 = tanh(qζ/kBT ) in the p-region, and
the nonequilibrium spin source of polarization δPn in the
n-region, at the edge of the depletion layer, determines
the I − V characteristics of the diodes. It is straight-
forward to generalize these considerations to include the
spin-polarized holes (Fabian et al., 2002b).
The dependence of the electric current j on qζ and
δPn was obtained by both numerical and analytical meth-
ods. Numerical calculations (Zˇutic´ et al., 2002) were per-
formed by self-consistently solving for the drift-diffusion,
continuity, as well as carrier recombination and spin-
relaxation equations, discussed in Sec. IV.A.4. While
the numerical calculations are indispensable in the high-
injection limit,117 valuable insight and analytical formu-
las can be obtained in the low-injection limit, where the
Shockley theory (Shockley, 1950) for ordinary p-n junc-
tions was generalized by Fabian et al. (2002b) for the
magnetic case.
To illustrate the I − V characteristics of MBD’s,
consider the low-injection limit in the configuration of
Fig. 30. The electron contribution to the total electric
current is (Fabian et al., 2002b)
jn ∼ n0(ζ)
[
eqV/kBT (1 + δPnPn0)− 1
]
, (114)
where V is the applied bias (positive for forward
bias) and n0(ζ) = (n2i /Na) cosh(qζ/kBT ) is the equi-
librium number of electrons in the p-region, depen-
dent on the splitting, the intrinsic carrier density
ni, and the acceptor doping Na. Equation (114)
generalizes the Silsbee-Johnson spin-charge coupling
(Johnson and Silsbee, 1985; Silsbee, 1980), originally
proposed for ferromagnet/paramagnet metal interfaces,
to the case of magnetic p-n junctions. The advantage
of the spin-charge coupling in p-n junctions, as opposed
to metals or degenerate systems, is the nonlinear voltage
dependence of the nonequilibrium carrier and spin den-
sities (Fabian et al., 2002b), allowing for the exponen-
tial enhancement of the effect with increasing V . Equa-
tion (114) can be understood qualitatively from Fig. 30
(Fabian et al., 2002b). In equilibrium, δPn = 0 and
117 The small bias or low-injection limit is the regime of applied bias
in which the density of the carriers injected through the depletion
layer (the minority carriers) is much smaller than the equilibrium
density of the majority carriers. Here and in Sec. IV.E.2 the
terms majority and minority refer to the relative carrier (electron
or hole) population and not to spin. The large bias or high-
injection limit is the regime where the injected carrier density
becomes comparable to the equilibrium density. This occurs at
forward biases comparable to the built-in potential, typically 1
V.

59
-2 -1 0 1 2
spin splitting/kBT
10-3
10-2
10-1
I (A
.cm
-
2 )
δP
n
=0
δP
n
=1
FIG. 31 Giant magnetoresistance (GMR) effect in magnetic
diodes. Current/spin-splitting characteristics (I-ζ) are calcu-
lated self-consistently at V=0.8 V for the diode from Fig. 30.
Spin splitting 2qζ on the p-side is normalized to kBT . The
solid curve corresponds to a switched-off spin source. The
current is symmetric in ζ. With spin source on (the extreme
case of 100% spin polarization injected into the n-region is
shown), the current is a strongly asymmetric function of ζ,
displaying large GMR, shown by the dashed curve. Materials
parameters of GaAs were applied. Adapted from Zˇutic´ et al.,
2002.
V = 0, no current flows through the depletion layer,
as the electron currents from both sides of the junction
balance out. The balance is disturbed either by apply-
ing bias or by selectively populating different spin states,
making the flow of one spin species greater than that of
the other. In the latter case, the effective barriers for
crossing of electrons from the n to the p side is different
for spin up and down electrons (see Fig. 30). Current
can flow even at V = 0 when δPn 6= 0. This is an exam-
ple of the spin-voltaic effect (a spin analog of the photo-
voltaic effect), in which nonequilibrium spin causes an
EMF (Zˇutic´ and Fabian, 2003; Zˇutic´ et al., 2002). In ad-
dition, the direction of the zero-bias current is controlled
by the relative sign of Pn0 and δPn.
MBD’s can display an interesting GMR-like effect,
which follows from Eq. (114) (Zˇutic´ et al., 2002). The
current depends strongly on the relative orientation of
the nonequilibrium spin and the equilibrium magnetiza-
tion. Figure 31 plots j, which also includes the contribu-
tion from holes, as a function of 2qζ/kBT for both the
unpolarized, δPn = 0, and fully polarized, δPn = 1, n-
region. In the first case j is a symmetric function of ζ,
increasing exponentially with increasing ζ due to the in-
crease in the equilibrium minority carrier density n0(ζ).
In unipolar systems, where transport is due to the major-
ity carriers, such a modulation of the current is not likely,
as the majority carrier density is fixed by the density of
dopants.
If δPn 6= 0, the current will depend on the sign of
Pn0 · δPn. For parallel nonequilibrium (in the n-region)
and equilibrium spins (in the p-region), most electrons
cross the depletion layer through the lower barrier (see
Fig. 30), increasing the current. In the opposite case
of antiparallel relative orientation, electrons experience a
larger barrier and the current is inhibited. This is demon-
strated in Fig. 31 by the strong asymmetry in j. The cor-
responding GMR ratio, the difference between j for par-
allel and antiparallel orientations, can also be calculated
analytically from Eq. (114) as 2|δPnPn0|/(1− |δPnPn0|)
(Fabian et al., 2002b). If, for example, |Pn0| = |δPn| =
0.5, the relative change is 66%. The GMR effect should
be useful for measuring the spin relaxation rate of bulk
semiconductors (Zˇutic´ et al., 2003), as well as for detect-
ing nonequilibrium spin in the nonmagnetic region of the
p-n junction.118
Although practical MBD’s are still to be fabri-
cated and the predicted effects tested, magnetic p-n
junctions have already been demonstrated. Indeed,
Wen et al. (1968)119 were perhaps the first to show
that a ferromagnetic p-n junction, based on the ferro-
magnetic semiconductor CdCr2Se4 doped with Ag ac-
ceptors and In donors, could act as a diode. Heav-
ily doped p-GaMnAs/n-GaAs junctions were fabri-
cated (Arata et al., 2001; Johnston-Halperin et al., 2002;
Kohda et al., 2001; Ohno et al., 2000b; Van Dorpe et al.,
2003a) to demonstrate tunneling interband spin injec-
tion. Incorporation of (Ga,Mn)As layer in the intrin-
sic region of p-i-n GaAs diode was shown to lead to an
efficient photodiode, in which the Mn ions function as
recombination centers (Teran et al., 2003). It would be
interesting to see such devices combined with a spin in-
jector in the bulk regions. Recently, Tsui et al. (2003)
have shown that the current in p-CoMnGe/n-Ge mag-
netic heterojunction diodes can indeed be controlled by
magnetic field. To have functioning MBD’s at room tem-
perature, and to observe the above predicted phenomena,
several important challenges have to be met:
(i) Zeeman or exchange splitting needs to sufficiently
large to provide equilibrium spin polarization, >∼ 1−10%.
This may be difficult at room temperature, unless the
effective g factor is ∼ 100 at B ∼ 1 T (Sec. II.D.3). The
use of ferromagnetic semiconductors is limited by their
TC (Sec. IV.B).
(ii) For a strong spin-charge coupling [recall the dis-
cussion of Eq. (114)] a nondegenerate carrier density is
desirable, which, while likely in (Zn,Cr)Te, is not eas-
ily realized in many other ferromagnetic semiconductors
that are typically heavily doped (Sec. IV.B).
(iii) An effective integration of magnetic and nonmag-
netic structures into single devices (Samarth et al., 2003)
is needed.
(iv) The samples need to be smaller than the spin dif-
118 This could be a way to detect spin injection into Si, where optical
detection is ineffective.
119 We thank M. Field for bringing this reference to our attention.

61
terfaces. However, the modulation of αBR by biasing
voltage (iii) has been already convincingly demonstrated
in In0.53Ga0.47As/In0.52Al0.48As QW’s (Grundler, 2000;
Hu et al., 1999; Nitta et al., 1997) [for GaAs/AlGaAs
2DEG see also (Miller et al., 2003)]. Initial experimen-
tal investigations of magnetoresistance in the Datta-Das
SFET systems were performed by Gardelis et al. (1999).
Recently spin precession in the the Datta-Das SFET, in-
cluding the bulk inversion asymmetry, was investigated
by (Winkler, 2004) using k · p model calculations. It is
not surprising that the conductance through the tran-
sistor, in the present orientation-dependent bulk inver-
sion asymmetry, depends rather strongly on the crys-
tallographic orientation of the two-dimensional channel
(Lusakowski et al., 2003). For more discussion of the
Dresselhaus bulk inversion asymmetry and the Bychkov-
Rashba structure asymmetry see Sec. III.B.2.b.
The Datta-Das SFET has generated great interest in
mesoscopic spin-polarized transport in the presence of
structure inversion asymmetry. Model calculations using
the tight-binding formulation of HSIA (recall Sec. II.B.2)
were reported by Pareek and Bruno (2002). Further the-
oretical investigations on the theme of the Datta-Das
spin transistor can be found in Matsuyama et al. (2002);
Nikolic´ and Freericks (2001) and in an extensive review
by Bournel (2000). Distinct SFET’s have also been
suggested, even in the absence of ferromagnetic regions
which are replaced by a rotating external magnetic field
of uniform strength (Wang et al., 2003a). Ciuti et al.
(2002b) proposed a ferromagnetic-oxide-semiconductor
transistor, with a nonmagnetic source and drain, but
with two ferromagnetic gates in series above the base
channel. The relative orientation of the gates’ magneti-
zation leads to magnetoresistance effects. An SFET that
can operate in the diffusive regime, in the presence of
both bulk and structure inversion asymmetry, has been
considered by Schliemann et al. (2003).
2. Magnetic bipolar transistor
The magnetic bipolar transistor (MBT) is a bipolar
transistor with spin-split carrier bands and, in general,
an injected spin (Fabian et al., 2002a; Fabian and Zˇutic´,
2004; Fabian et al., 2004). A related device structure
was already proposed by Gregg et al. (1997) in a push
for silicon-based spintronics. In this proposal (also called
SPICE for spin-polarized injection current emitter) the
semiconductors have no equilibrium spin, while the spin
source is provided by a ferromagnetic spin injector at-
tached to the emitter, and another ferromagnetic metal,
a spin detector, is attached to the base/collector junction
to modulate the current flow. In both configurations the
aim is to control current amplification by spin and mag-
netic field.
A scheme of a particular MBT is shown in Fig. 32.
Such a three-terminal device can be thought of as con-
sisting of two magnetic p-n junctions connected in se-
p base
−V
−V
I IB CI E
n emitter n collector
bi
biV
V BC
BE
2qζ
Eg
FIG. 32 Scheme of an n-p-n magnetic bipolar transistor
with magnetic base (B), nonmagnetic emitter (E), and col-
lector (C). Conduction and valence bands are separated by
the energy gap Eg. The conduction band has a spin split-
ting 2qζ, leading to equilibrium spin polarization PB0 =
tanh(qζ/kBT ). Carriers and depletion regions are represented
as in Fig. 30. In the so called forward active regime, where the
transistor can amplify currents, the E-B junction is forward
biased (here with voltage VBE > 0 lowering the built-in poten-
tial Vbi), while the B-E junction is reverse biased (VBC < 0).
The directions of the current flows are indicated. Electrons
flow from E to B, where they either recombine with holes
(dashed lines) or continue to be swept by the electric field
in the B-E depletion layer towards C. Holes form mostly the
base current, IB, flowing to the emitter. The current amplifi-
cation β = IC/IB can be controlled by PB0 as well as by the
nonequilibrium spin in E. Adapted from Fabian et al., 2004.
ries. Materials considerations discussed in Sec. IV.D
also apply to an MBT in order to provide a sufficient
equilibrium polarization in a magnetic base PB0. While
nonmagnetic, the emitter has a nonequilibrium polariza-
tion δPE from a spin source, similar to the magnetic
diode case in Fig. 30. Only the spin polarization of
electrons is assumed. Applying the generalized Shock-
ley theory to include spin effects (Fabian et al., 2002b), a
theory of MBT was developed by Fabian et al. (2002a);
Fabian and Zˇutic´ (2004). Later, simplified schemes of
MBT [not including the effect of nonequilibrium spin
(δPE = 0)] were also considered by Flatte´ et al. (2003)
and Lebedeva and Kuivalainen (2003).
The current amplification (gain) β = IC/IB (see
Fig. 32) is typically ∼ 100 in practical transistors. This
ratio depends on many factors, such as the doping densi-
ties, carrier lifetimes, diffusion coefficients, and structure
geometry. In an MBT β also depends on the spin split-
ting 2qζ (see Fig. 32) and the nonequilibrium polariza-
tion δPE . This additional dependence of β in an MBT
is called magnetoamplification (Fabian and Zˇutic´, 2004).
An important prediction is that the nonequilibrium spin
can be injected at low bias all the way from the emitter,
through the base, to the collector (Fabian et al., 2002a;
Fabian and Zˇutic´, 2004) in order to make possible an ef-
fective control of β by δPE .
The calculated dependence of the gain on the spin
splitting for δPE = 0.9 is shown in Fig. 33, for GaAs and
Si materials parameters. The gain is very sensitive to the

62
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
base spin splitting (in kBT)
0
100
200
300
400
500
600
ga
in
Si
GaAs
FIG. 33 Calculated gain dependence of an MBT as a func-
tion of base spin splitting 2qζ, given in units of thermal energy
kBT . The nonequilibrium spin polarization in the emitter is
δPE = 0.9. Si (solid) and GaAs (dashed) materials parame-
ters were applied. Adapted from Fabian et al., 2002a.
equilibrium magnetization in Si, while the rapid carrier
recombination in GaAs prevents more effective control
of the transport across the base. In Si it is the spin
injection at the emitter-collector depletion layer which
controls the current. As the spin-charge coupling is most
effective across the depletion layer (see Sec. IV.D), this
coupling is essential for the current in Si. In the limit of
slow carrier recombination (Fabian et al., 2002a),
β ∼ cosh(qζ/kBT )(1 + δPEPB0). (116)
Both magnetic field (through ζ) and nonequilibrium spin
affect the gain, an implication of the spin-voltaic effect
(Zˇutic´ and Fabian, 2003; Zˇutic´ et al., 2002). The sensi-
tivity of the current to spin can be used to measure the
injected spin polarization. If no spin source is present
(δPE = 0), there is no spin-charge coupling in the space-
charge regions, unless at least two regions are magnetic.
The only remaining effects on the I − V characteristics
come from the sensitivity of the carrier densities in the
equilibrium magnetic regions to ζ [see Eq. (116) for the
case of δPE = 0].
The MBT is, in effect, a magnetic heterostructure tran-
sistor, since its functionality depends on tunability of the
band structure of the emitter, base, or collector. The ad-
vantage of MBT, however, is that the band structure is
not built-in, but can be tuned during the device oper-
ation by magnetic field or spin injection signals. The
challenges to demonstrate the predicted phenomena in
MBT are similar to those of magnetic bipolar diodes, see
Sec. IV.D.
3. Hot-electron spin transistors
Spin transistors that rely on transport of hot (non-
thermalized) carriers have the potential to serve of sev-
eral different purposes. On the one hand, they could
be used as a diagnostic tool to characterize spin- and
energy-dependent interfacial properties, scattering pro-
cesses, and electronic structure, relevant to spintronic de-
vices.120 On the other hand, hot-electron transistors are
also of interest for their ability to sense magnetic fields,
their possible memory applications, and a their potential
as a source of ballistic hot-electron spin injection. Be-
low we discuss two representative examples, a spin-valve
transistor and a magnetic tunneling transistor.
The spin-valve or Monsma transistor provided an
early demonstration of a hot-electron spin transis-
tor and realization of a hybrid spintronic device that
integrates metallic ferromagnets and semiconductors
(Monsma et al., 1995, 1998). A three terminal struc-
ture 121 consisted of a metallic base (B) made of a
ferromagnetic multilayers in a CPP geometry [as de-
picted in Fig. 3(a)] surrounded by a silicon emitter (E)
and collector (C) with two Schottky contacts, formed
at E/B and B/C interfaces.122 Forward bias VEB con-
trols the emitter current IE of spin-unpolarized elec-
trons, which are injected into a base region as hot car-
riers. The scattering processes in the base, together
with the reverse bias VBC , influence how many of the
injected electrons can overcome the B/C Schottky bar-
rier and contribute to the collector current IC . Simi-
lar to the physics of GMR structures (Gijs and Bauer,
1997; Levy and Mertig, 2002) scattering in the base re-
gion strongly depends on the relative orientation of the
magnetizations in the ferromagnetic layers. Electrons
with spin which has magnetic moment opposite (an-
tiparallel) to the magnetization of a ferromagnetic layer
typically are scattered more than electrons with paral-
lel magnetic moments, resulting in a spin-filtering ef-
fect which can be described in terms of spin-dependent
mean free path (Hong and Mills, 2000; Pappas et al.,
1991; Rendell and Penn, 1980). Generally, both elastic
120 These efforts are motivated in part by the success of
(spin-insensitive) ballistic-electron-emission microscopy in
providing high spatial and energy resolution of proper-
ties of metal/semiconductor interfaces (Bonnell Ed., 2001;
Kaiser and Bell, 1988; Smith et al., 2000). A subsequent
variation–a ballistic-electron-magnetic microscopy, which
also uses an STM tip to inject hot carriers, is capable
of resolving magnetic features at a ∼ 10 nm length scale
(Rippard and Buhrman, 1999, 2000).
121 Similar to other hot-electron spin devices, the term transistor
characterizes their three-terminal structure rather than the usual
functionality of a conventional semiconductor transistor. In par-
ticular, a semiconductor bipolar transistor, which also has an
emitter/base/collector structure, typically has a sizable current
gain–a small change in the base current leads to a large change
in the collector current (see Sec. IV.E.2). However, only a small
current gain ∼ 2 (due to large current in a metal base) was pre-
dicted in magnetic tunnel-junction-based devices (Hehn et al.,
2002).
122 Another realization of a spin-valve transistor combines a GaAs
emitter with a Si collector (Dessein et al., 2000).

66
FIG. 36 (a) Nanopilar device: schematic diagram of a nanopi-
lar device operating at room temperature. The direction of
magnetization is fixed (pinned) in the thick Co film and free in
the thin Co film; (b) differential resistance dV/dI of a nanopi-
lar device as a function of applied field; (c) dV/dI of the de-
vice as a function of applied current. The arrows in panels (b)
and (c) represent the direction of magnetic field and current
sweeps, respectively. For positive current, electrons flow from
the thin to the thick Co film. Adapted from Albert et al.,
2002.
various realizations of an all-optical NMR. The role
of the resonant radio waves is played by periodi-
cally optically excited electron spins (Eickhoff et al.,
2002; Fleisher and Merkulov, 1984b; Kalevich, 1986;
Kalevich et al., 1980, 1981; Kikkawa and Awschalom,
2000; Salis et al., 2001a). Electron-nuclear spintronics is
likely to become relevant for quantum computation and
for few-spin manipulations, which can benefit from long
nuclear spin coherence times (even lasting minutes).
The range of potential spintronic applications goes
beyond the use of large magnetoresistive effects.
Rudolph et al. (2003), for example, have demonstrated
the operation of a spin laser. The laser is a vertical-cavity
surface-emitting laser (VCSEL), optically pumped in the
gain medium, here two InGaAs quantum wells, with 50%
spin-polarized electrons. The electrons recombine with
heavy holes, which are effectively unpolarized, emitting
circularly polarized light (see Sec. II.B). The threshold
electrical current, extracted from the pump power for the
lasing operation, was found to be 0.5 A·cm−2, which is
23% below the threshold current of the spin-unpolarized
VCSEL. Furthermore, for a fixed pump power, the emis-
sion power of the laser changed by 400% upon chang-
ing the degree of circular polarization of the pump laser.
The reason for the decrease in threshold is the selective
coupling of spin-polarized electrons to photons with one
helicity. While the experiment was conducted at 6 K, a
room-temperature operation and an electrically pumped
laser should be viable as well.129
129 The requirement is that the spin relaxation time be longer than
the carrier recombination time, and that the spin injection spot
The demonstration that the flow of spin-polarized car-
riers, rather than applied magnetic field, can also be
used to manipulate magnetization of ferromagnetic ma-
terials brings the exciting prospect of a novel class of
spintronic devices. In addition to reversal of magneti-
zation, which is a key element in realizing various mag-
netoresitive applications, the driving of a spin-polarized
current can lead to coherent microwave oscillations
in nanomagnets (Kiselev et al., 2003). Spin-transfer
torque (Sec. I.B.1) has already been realized in sev-
eral experimental geometries. These include nanowires
(Kelly et al., 2003; Wegrowe et al., 1999), point con-
tacts (Ji et al., 2003; Tsoi et al., 1998, 2000, 2002),
nanoconstrictions (Myers et al., 1999; Rippard et al.,
2004), and nanopilars (Albert et al., 2002; Katine et al.,
2000; Urazhdin et al., 2003) (see Fig. 36), all involving
metallic ferromagnets. The common feature of all these
geometries is a need for very large current densities (∼
107 Acm−2). Ongoing experiments (Chiba et al., 2004;
Munekata, 2003; Yamanouchi et al., 2004) to demon-
strate spin-transfer torque (together with other coopera-
tive phenomena) in ferromagnetic semiconductors, which
have much smaller magnetization than their metallic
counterparts, are expected to also require much smaller
switching currents. Based on the findings in electric-
field controlled ferromagnetism (see Fig. 27), it has
been demonstrated that the reversal of magnetization in
(In,Mn)As can be manipulated by modifying the car-
rier density, using a gate voltage in a FET structure
(Chiba et al., 2003).
Acknowledgments
We thank R. H. Buhrman, K. Bussmann, R. de Sousa,
M. I. D’yakonov, S. C. Erwin, M. E. Fisher, A. M. Gold-
man, K. Halterman, X. Hu, S. V. Iordanskii, M. Johnson,
B. T. Jonker, K. Kavokin, J. M. Kikkawa, S. Maekawa,
C. M. Marcus, I. I. Mazin, B. D. McCombe, J. S. Mood-
era, H. Munekata, B. E. Nadgorny, H. Ohno, S. S. P.
Parkin, D. C. Ralph, E. I. Rashba, W. H. Rippard, V. I.
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work was supported by DARPA, the US ONR, and the
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2DEG two dimensional electron gas
BAP Bir-Aronov-Pikus
BCS Bardeen Cooper Schrieffer
BIA bulk inversion asymmetry
BTK Blonder-Tinkham-Klapwijk
CESR conduction electron spin resonance
CIP current in plane
CMOS complementary metal oxide semiconductor
CMR colossal magnetoresistance
CPP current perpendicular to plane
DNA deoxyribonucleic acid
DP D’yakonov-Perel’
EDSR electron dipole spin resonance
EMF electromotive force
ESR electron spin resonance
EY Elliot-Yafet
F ferromagnet
FSm ferromagnetic semiconductor
GMR giant magnetoresistance
FET field effect transistor
HFI hyperfine interaction
I insulator
HTSC high temperature superconductor
LED light emitting diode
MBD magnetic bipolar diode
MBE molecular beam epitaxy
MBT magnetic bipolar transistor
MC magnetocurrent
MR magnetoresistance
MRAM magnetic random access memory
MTJ magnetic tunnel junction
N normal (paramagnetic) metal
NMR nuclear magnetic resonance
QD quantum dot
QPC quantum point contact
QW quantum well
S superconductor
SET single electron transistor
SFET spin field effect transistor
SIA structure inversion asymmetry
Sm semiconductor
SQUID superconducting interference quantum device
STM scanning tunneling microscope
TESR transmission electron spin resonance
TABLE II List of acronyms used in the text.