Intrinsic frequency doubling in a magnetic tunnel junction–based
spin torque oscillator
P. K. Muduli,1,a) O. G. Heinonen,2,3 and Johan A˚kerman1,4
1Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden
2Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
3Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208-3112, USA
4Materials Physics, School of ICT, KTH- Royal Institute of Technology, Electrum 229, Kista 164 40, Sweden
(Received 10 August 2011; accepted 31 August 2011; published online 13 October 2011)
We show that the frequency of a magnetic tunnel junction (MTJ)-based spin torque oscillator (STO)
can be doubled and the first harmonic entirely suppressed by orienting the free and fixed layer
magnetizations in an antiparallel (AP) state. The angular dependence of the harmonics allows us to
extract the free layer precession angle, which follows a parabolic decrease from a maximum of 20
in the AP state to about 10 at 25 of misalignment. Frequency-doubling provides both a promising
way for increasing the frequency of MTJ-STOs and a means for high-rate frequency shift keying
using only a small magnetic field.VC 2011 American Institute of Physics. [doi:10.1063/1.3647759]
Spin transfer torque (STT) can induce magnetization
reversal or steady-state precession at well-defined GHz fre-
quencies in a magnetic nanostructure.1–4 The latter effect can
be used in so-called spin-torque oscillators (STOs).5 The
attractive features of STOs include a very large frequency
tuning range,6,7 efficient spin-wave emission in magnonic
devices,8 very high modulation rates,9–15 a sub-micron device
size,18 and straightforward integration with semiconductor
technology.19,20 The basic structure of a STO is either a metal-
lic spin valve (SV) or a magnetic tunnel junction (MTJ) with
an oxide barrier, such as MgO. MTJ-STOs based on CoFeB/
MgO/CoFeB have attracted considerable interest recently
because the microwave power is usually much higher com-
pared to all-metallic SV-STOs.21–24 Two disadvantages of
MTJ-STOs are the limited frequency tunability with respect to
current and the limited frequency tuning range compared to
all-metallic SV STOs. While the field tunability (50 GHz/T)
is comparable to that of nanocontact metallic STOs,6,7,25 the
power of the signal decreases drastically with increasing field
strength, which limits the practical frequency tuning range.
Here, we explore a method of increasing the frequency
of an MgO based MTJ-STO using intrinsic frequency dou-
bling when the magnetization of the free layer (FL) and the
reference layer (RL) are antiparallel (AP). Using a macrospin
model21 for the angular dependence of the first and second
harmonic, we extract the FL precession angle, which exhibits
a parabolic dependence on misalignment from the AP state.
We finally suggest how to exploit the intrinsic frequency
doubling for high-rate frequency shift keying using a small
modulated magnetic field perpendicular to the larger static
field.
The structure of the devices is IrMn(5 nm)/CoFe
(2.1 nm)/Ru(0.81 nm)/CoFe(1 nm)/CoFeB(1.5 nm)/MgO(1nm)/
CoFeB (3.5 nm). The antiferromagnetic IrMn layer provides
an exchange bias on the adjacent CoFe-pinned layer, which
couples antiferromagnetically through Ru to the composite
CoFe/CoFeB RL. Above the MgO tunnel barrier is the
CoFeB FL, the magnetization of which can be easily rotated
by an external field. Details about the fabrication methods of
the structures can be found elsewhere.22,26 We here discuss
results from a circular device with an approximate diameter
of d¼ 240 nm. Similar results were obtained in other devices
of same dimensions, as well as in devices with d¼ 65 nm
and 180 nm. The resistance-area product in the parallel state
is about 1.5 X lm2. The measurement system is similar to that
described in Refs. 7 and 24, except that, in the present work, a
projected field magnet mounted on a stepper motor was used to
vary the in-plane field angle u continuously. The amplifier had
a gain of þ33dB and working range of 0.1-18GHz.
Figure 1 shows the measured spectra at three different
field angles for a constant current I ¼ 8 mA and constant
field magnitude of H ¼ 400 Oe. We use the convention that
a positive current flows from the FL to the RL (electrons
flow from the RL to the FL). For this polarity and field
strength, STT induces precession of the FL.24 The equilib-
rium direction of the RL is along the positive x^ -axis. Hence,
at u ¼ 180 in Fig. 1, the FL magnetization is AP to that of
the RL. As can be seen from the figure, the first harmonic
signal at u ¼ 180 is significantly suppressed compared to
u ¼ 160 and u ¼ 200.
The angular dependence of the integrated power of the
first and second harmonic signals is shown in Fig. 2(a) for
I¼ 8 mA and H¼ 400Oe. The integrated power is corrected
for losses in the transmission line and for reflections at the
STO due to impedance mismatch between the STO and the
50 X probe. These losses were calculated using the measure-
ment of scattering matrix element S11 following the method dis-
cussed in Refs. 10, 21, and 27. The inset of Fig. 2(b) shows the
measured S11. The power of the first harmonic signal is sup-
pressed near u ¼ 180, whereas that of the second harmonic
signal is enhanced. In Fig. 2(b) is shown a plot of dc resistance
R versus field angle along with a calculation of R according to
the cosine dependence28 of the tunneling magnetoresistance
(TMR): R ¼ Rp þ 0:5ðRap  RpÞð1 cos hrÞ. Here, Rap (Rp)a)Electronic mail: pranaba.muduli@physics.gu.se.
0021-8979/2011/110(7)/076102/3/$30.00 VC 2011 American Institute of Physics110, 076102-1
JOURNAL OF APPLIED PHYSICS 110, 076102 (2011)
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denotes the measured resistance in AP-state (P-state) and hr
denotes the equilibrium relative angle between FL and RL
magnetizations. Figure 2(b) shows that the applied field angle
u coincides with hr within the accuracy of the experiment and
that the FL and RL magnetizations are perfectly antiparallel
near u ¼ 180. The frequency doubling and the suppression of
the first harmonic signal occur near the perfect AP alignment.
The power of the 2nd harmonic signal reached to 1.25 nW near
u ¼ 180, which is one order of magnitude higher than the cor-
responding power of all-metallic spin valve devices.6,11
In order to understand this behavior, we consider a mac-
rospin model, as developed in Refs. 21 and 29. According to
this model, the power in the 1st and 2nd harmonic signals
are given by the following equations:
Pf ¼ gðfÞ
Rap  Rp
2
 2
J21ðhpÞ sin2 hr
R0I2
8
 
; (1)
P2f ¼ gð2fÞ
Rap  Rp
2
 2
J22ðhpÞ cos2 hr
R0I2
8
 
: (2)
Here, hp denotes the precession angle of the FL magnetiza-
tion and R0 denotes the dc component in the total resistance
of the device and depends on Rap, Rp, hr, and hp, as defined
in Ref. 21. J1 and J2 denote the Bessel functions of the first
kind. The pre-factors gðfÞ and gð2fÞ relate the measured
power to the actual power emitted by the STO. The above
equation can qualitatively explain the mechanism of fre-
quency doubling at u ¼ 180: the power of the first har-
monic vanishes at 180, since Pf is proportional to sin
2 hr;
the power of the second harmonic signal increases, since P2f
is proportional to cos2hr. Both of these behaviors are in good
qualitative agreement with experiment. Note that, in the
studied range, u ¼ hr. The physical picture of the frequency
doubling phenomena is as follows: For in-plane FL equilib-
rium magnetization, the precession trajectory is elliptical,30
with the major axis of the ellipse in-plane and the minor axis
perpendicular to the plane of the layers, as shown in the inset
of Fig. 2(a). At u ¼ 180, the RL and FL magnetizations are
anti-parallel and the resistance along the trajectory has mini-
mum (maximum) at the antipodal points of the major (minor)
axis. Consequently, during a single precession period, the re-
sistance will twice attain both its minimum and maximum
values and the frequency of the resistance (or voltage) will
be twice the precessional frequency. Similar behavior has
been mentioned for an all-metallic spin valve nanopillar de-
vice with a thick fixed layer,31 though both the oscillation
frequency and the power were significantly lower than in the
present work.
For a quantitative comparison, we use the fact that the
relative angle between the FL and RL obtained from the
R–H loop is equal to the field angle. By dividing Eq. (1) by
Eq. (2), we obtain
Pf
P2f
¼ gðfÞ
gð2fÞ
J21ðhpÞ
J22ðhpÞ
tan2ðhrÞ: (3)
The values of gðfÞ and gð2fÞ were determined from the S11
measurement [as shown in the inset of Fig. 2(b)]. We then fit
Eq. (3) to the measured power ratio to obtain hp, which
ranges from about 20 at AP condition to about 10 at field
angles (or relative angles) of 155 and 205, as shown in
Fig. 3. The angular dependence of hp can be described by
a parabolic dependence: hp ¼ aðhr  180Þ2 þ b, where
a ¼ 0:015 and b ¼ 20, as shown in the inset of Fig. 3. This
value of precession angles is in the same range as observed
in other works.21,22 We have also verified the magnitude and
quadratic decrease in the precession angle away from AP
configuration using micromagnetic simulations.
It is noteworthy that the observed frequency doubling is
purely geometrical in nature and does not involve any mode
change or large current tuning. The frequency doubling
originates from a change in the angular function of the
FIG. 2. (Color online) (a) Integrated power of first (black squares) and sec-
ond (red circles) harmonic vs in-plane field angle, u, at H¼ 400Oe and
I¼ 8 mA. (b) Experimental (open circles) and calculated resistance (solid
line) vs u at H¼ 400Oe. The inset shows the network analyzer scattering
parameter S11, also measured at H¼ 400Oe and I¼ 8 mA.
FIG. 1. (Color online) Power spectral density at three different field angles
for I ¼ 8 mA and H ¼ 400 Oe.
076102-2 Muduli, Heinonen, and A˚kerman J. Appl. Phys. 110, 076102 (2011)
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

magnetoresistance, onto which the essentially unchanged pre-
cessional state is mapped. This opens up for the intriguing
possibility of modulating the output of a MTJ-STO by as
much as 5GHz, while allowing the MTJ-STO free layer to
precess in a coherent and largely unperturbed steady state. As
Fig. 2 shows, one needs to change the applied field angle by
about 20 to switch completely between the first and second
harmonic. For the MTJ-STO studied here, high data rate fre-
quency shift keying (FSK) at approximately 5 and 10GHz
would, hence, be possible by applying a static field of 400Oe
at 170 and a modulating field of 70Oe perpendicular to the
static field, which provides the necessary 610 deflection.
We note that FSK has been demonstrated in vortex-based
STOs9,15 by current modulation up to a data rate of 10MHz.
However, our proposed field-modulated FSK has the poten-
tial for a much higher data rate (>1 GHz), due to the large
difference in the two frequencies (5 GHz).
In conclusion, we have shown that the frequency of an
MTJ-based STO can be doubled when the magnetizations of
the free and fixed layers are perfectly antiparallel. The
behavior of the power in the first and second harmonics can
be explained on the basis of a macrospin model, and we
obtain a maximum precession angle of about 20 at AP
alignment and a parabolic reduction for increasing misalign-
ment. The frequency doubling behavior provides a promising
way for increasing the operational frequencies of STOs as
well as opening up for field-controlled frequency shift key-
ing at high data rates.
Support from the Swedish Foundation for Strategic
Research (SSF), the Swedish Research Council (VR), the
Go¨ran Gustafsson Foundation, and the Knut and Alice Wallen-
berg Foundation are gratefully acknowledged. J.A˚. is a Royal
Swedish Academy of Sciences Research Fellow supported by a
grant from the Knut and Alice Wallenberg Foundation.
Argonne National Laboratory is operated under Contract No.
DE-AC02-06CH11357 by UChicago Argonne, LLC.
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FIG. 3. (Color online) Measured ratio (black filled circles) Pf=P2fvs u and
fit (red solid line) according to Eq. (3). The inset shows calculated preces-
sion angle hp versus the relative angle hr and a parabolic fit (red solid line).
076102-3 Muduli, Heinonen, and A˚kerman J. Appl. Phys. 110, 076102 (2011)
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp