demand or costs or damages whatsoever or howsoever caused arising directly or indirectly
in connection with or arising out of the use of this material.
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Integrated Ferroelectrics, 125:147–154, 2011
Copyright © Taylor & Francis Group, LLC
ISSN: 1058-4587 print / 1607-8489 online
DOI: 10.1080/10584587.2011.574478
Spin Torque Oscillators and RF Currents—
Modulation, Locking, and Ringing
P. K. MUDULI,1 YE. POGORYELOV,2 Y. ZHOU,2
FRED MANCOFF,3 AND JOHAN ÅKERMAN4,∗
1Physics Department, University of Gothenburg 412 96, Gothenburg, Sweden
2Materials Physics, Royal Institute of Technology, Electrum 229,
164 40 Kista, Sweden
3Everspin Technologies, Inc., 1300 N. Alma School Road, Chandler,
Arizona 85224, USA
4Physics Department, University of Gothenburg, 412 96 Gothenburg,
Sweden and Materials Physics, Royal Institute of Technology, Electrum 229,
164 40 Kista, Sweden
We study the interaction between a nano-contact spin torque oscillator (STO) and
injected radio-frequency and microwave currents. Modulation of the STO signal is
observed over a wide frequency range from 100 MHz to 3.2 GHz. The modulation side-
bands agree well with macrospin simulations. When the injected microwave frequency
approaches that of the STO, we observe injection locking, frequency pulling/pushing,
and intermodulation peaks. While the intermodulation peaks are reasonably well repro-
duced by macrospin simulations, they do not follow the Adler’s model. We argue that
this discrepancy is due to intrinsic ringing effects stemming from the internal dynamics
of the STO.
While spintronics started with the discovery of giant magnetoresistance [1, 2] (GMR)
in 1988, which was used in hard-drive read-heads [3] from about 1997 until over-
taken by read-heads based on tunneling magnetoresistance (TMR), the last decade has
seen an explosive growth in the interest in spintronics. This has largely been due
to the prediction [4, 5] and experimental confirmation [6, 7] of spin torque transfer
(STT), the observation of large TMR in MgO based Magnetic Tunnel Junctions [8–12],
and the realization of additional commercially viable integrated spintronic applications,
such as Magnetoresistive Random Access Memory (MRAM) [13, 14]. While STT is heav-
ily researched for next generation MRAM [15–17], it can also be used to realize microvave
signal generators [18–22], modulators [23, 24], and detectors [25–27]. The central nano
device is the so-called spin-torque oscillator (STO), which is currently attracting a rapidly
growing interest since it offers a unique combination of critically important microwave
properties such as ultrawide band frequency operation, extremely small footprint, and easy
integration using well-established MRAM fabrication and integration processes.
Received September 2, 2010; in final form October 29, 2010.
∗Corresponding author. E-mail: johan.akerman@physics.gu.se
[325]/147
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148/[326] P. K. Muduli et al.
The working principle of an STO is that of a magnetoresistive device where a spin
polarized current excites the free layer into coherent precession, which in turn generates an
oscillatory resistance in the GHz frequency range, either through GMR or TMR depending
on the type of device. Since typically a constant drive current is passed through such a
device, it outputs an oscillatory voltage signal in the microwave frequency range, due
to the oscillating device resistance. The excitation is essentially identical to the intrinsic
ferromagnetic resonance (FMR) of the precessing magnetic layer and is driven by the
transfer of angular momentum from the spin-polarized electrons to the local free layer
magnetization. The effect usually occurs in a nanoscale device where a current density of
the order of 108 A/cm2 first gets spin-polarized by passing through the fixed magnetic layer
and then drives the precession of the free layer magnetization.
While the first STOs were either GMR nano-pillars[7] or nano-contacts on top of
extended GMR trilayers [28], where the easy direction of both magnetic layers were in
the film plane, a wide range of additional architectures have been proposed [19, 29–32]
and experimentally realized [33–36]. In this study we focus on the traditional nano-contact
based STO where a nano-contact of about 100 nm drives a high local current density
through an extended GMR trilayer mesa. Both theory and micromagnetic simulations have
shown that two qualitatively different spin wave modes are responsible for the output
signal, depending on the applied magnetic field angle. For a perpendicularly magnetized
STO free layer (typically achieved by applying an out-of-plane field of the order of 1 T),
only a propagating spin wave mode is allowed [37]. If the applied field angle is moved
towards the film plane, there exists a critical angle below which both localized and non-
propagating modes are allowed [38–40]. This so-called spin wave bullet was very recently
unambiguously confirmed in detailed angular dependent measurements [41].
A schematic of the device structure is shown in Fig. 1a. Using e-beam lithography, a
circular Al nanocontact with nominal diameter of 130 nm was fabricated through a SiO2
insulating layer, onto a 8 × 26 µm2 pseudo-spin-valve mesa consisting of Si/SiO2/Cu(25
Figure 1. (a) Schematic of the sample structure of a nano-contact based spin torque oscillator
device along with its operating principle. (b) Typical output spectrum from an STO measured using
a spectrum analyzer. The STO operating frequency is 16 GHz and its linewidth, extracted from a
Lorentzian fit (solid line), is about 12.5 MHz.
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Spin Torque Oscillators and RF Currents [327]/149
nm)/Co81Fe19 (20 nm)/Cu (6 nm)/Ni80Fe20 (4.5 nm)/Cu (3 nm)/Pd (2 nm). Details of the
sample fabrication can be found in Ref. [42]. We apply a d.c. bias current to the device
so that electrons flow from the free (precessing) layer (Ni80Fe20) to the fixed (Co81Fe19)
magnetic layer. To detect the generated microwave signal, we use custom-designed non-
magnetic 50 Ohm, 40 GHz ground-signal-ground (GSG) microwave probes from GGB
industries. The signal was amplified using a broadband 16–40 GHz, +20 dB microwave
amplifier, and finally detected by a spectrum analyzer with an upper frequency limit of
46 GHz. The d.c. current was fed to the device by a precision current source, through a
dc-40 GHz bias tee connected in parallel with the transmission line.
We inject an external RF/microwave signal to the STO via a circulator. In the mod-
ulation experiments, the injected signal was swept from 10 MHz to 4 GHz, whereas for
injection locking, it was swept in a range close to the operating frequency of the STO. The
injected power at the STO is typically lower than the nominal value due to (i) losses in the
transmission line, and (ii) reflections at the STO due to impedance mismatch between
the STO and the 50 Ohm GSG probe. These losses were calculated using the measurement
of scattering matrix element S11 as discussed in Ref [23]. Since all experiments were done
in fields applied close to the STO film normal (about 80◦ w.r.t. the film plane), all STO
signals presented in this paper reflect the properties of the propagating spin wave mode. In
this geometry we also obtain the maximum signal power of the STO [42].
Figure 1b shows a typical output spectrum from one of our devices. The operating
frequency is centered at 16 GHz and the power spectral density shows a Lorentzian line
shape with a full width at half maximum (FWHM) of 12.5 MHz. The total integrated power
is 200 pW, which is quite typical for nano-contact and GMR based STOs.
Figure 2 demonstrates the wide tuning range of this device from about 12 to 26 GHz.
Both the drive current and the applied magnetic field can be used to tune the operat-
ing frequency, and both parameters show quite linear transfer functions of about KI =
120 MHz/mA and KH = 18.5 MHz/mT respectively (the field angle can also be used to
Figure 2. Field and current dependence of the STO frequency measured at a field angle of about
80◦.
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150/[328] P. K. Muduli et al.
tune the operating frequency [28], with extrapolations indicating operating frequencies as
high as 65 GHz [43]).
When a RF current is superimposed on the drive current, the STO signal is modulated
around its d.c. operating point. As for any ordinary oscillator, rapid modulation leads to
the formation of sidebands with an equidistant spacing given by the modulation frequency.
Under modulation, the total power is divided up between the main peak (carrier) and the
sidebands with RF amplitude dependent proportions given by a series of Bessel functions.
Since the frequency vs. current relation of an STO often shows stronger non-linearities than
in Fig. 2, non-linear frequency modulation theory has been applied to describe the sideband
powers [25]. Since not only the frequency, but also the STO amplitude depends on the
current, amplitude modulation must also be taken into account, and it was recently shown
that a combined non-linear frequency and amplitude modulation theory gives an essentially
perfect agreement without any free parameters [23]. Figure 3a shows both a free-running
STO (no modulation) and the development of modulation sidebands using two different
modulation frequencies. In Fig. 3b we push the modulation frequency up to 3.2 GHz where
we can still observe appreciable sideband power. The STO hence lends itself to very high
modulation frequencies and shows great potential as ultra-high data transmitters.
If instead of modulating the STO, we inject a microwave frequency close to the STO
operating frequency, it is possible to induce injection locking [45, 46]. This is shown in
Fig. 4a where the STO frequency is held constant at 20 GHz and an injected microwave
frequency is scanned from 19.5 to 20.5 GHz. As the injected signal approaches 20 GHz,
the STO first gets pulled down in frequency and finally locks on to the injected signal.
In the locked state, the linewidth of the STO approaches that of the injected signal. On
approach to locking, the STO develops strong intermodulation sidebands. The 3rd order
intermodulation products are clearly seen at their expected frequencies (IM3+ = 2finj −
fSTO; IM3− = 2fSTO − finj). One of the 5th order intermodulation products can also be
observed at IM5− = 3fSTO − 2finj). In Fig. 4b we show macrospin simulations of the same
measurement. The qualitative agreement between the experiment and the simulation is
quite remarkable. According to standard intermodulation theory, the amplitudes of the 3rd
Figure 3. Spectral output of the STO at different modulating frequencies for a modulation current
of 1.2 mA. (a) Spectral output with no modulation, and modulation frequencies of 200 MHz and
500 MHz showing the equally spaced sidebands. (b) spectral output at higher modulating frequencies
of 1.5, 2.5 and 3.2 GHz.
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Spin Torque Oscillators and RF Currents [329]/151
Figure 4. (a) Experimental map of measured STO power (in dB) versus STO frequency and in-
jected RF frequency showing injection locking and intermodulation. (b) Corresponding Macrospin
simulation of locking and intermodulation using experimental parameters.
order products are given by
A(2fST O−fRF ) ≈ a3 · A
2
ST O · ARF
A(2fRF −fST O ) ≈ a3 · AST O · A
2
RF
where a3 is a frequency dependent prefactor. By taking the ratio of the two 3rd order
products we get the intermodulation ratio
IM+3
IM−3
≡
A(2fRF −fST O )
A(2fST O−fRF )
=
(
ARF
AST O
)
which can be used to perform a simple test of whether the products follow the expected
amplitude dependence. In Fig. 5 we vary the injected RF power and plot the intermodulation
ratio as a function of the injected power for two injected frequencies 20.15 and 20.25 GHz.
As can clearly be seen, the intermodulation ratio shows a much weaker dependence on
injected power than expected. Instead of increasing linearly with the injected amplitude,
it is essentially constant. The intermodulation peak amplitudes seem to have saturated as
Figure 5. Ratio of third-order intermodulation products (left scale, black squares) and ratio of power
of STO and power of RF signal (right scale, gray circles) at fixed injected frequency of (a) 20.15 GHz
and (b) 20.25 GHz.
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152/[330] P. K. Muduli et al.
a function of injected power. Using macrospin simulations [47–51] it was recently shown
that injection locking is expected to only follow the classical Adler’s model for very
low injection currents [52]. Above a critical injection power, the locking rate no longer
increases. Instead, the locking rate saturates and internal ringing of the locked state takes
place. It is possible that the experimentally observed saturation of intermodulation is due
to the same mechanism. Above a certain injected power, the STO can no longer respond
in a proportional way and the intermodulation peaks cease to grow with the injected
power.
In conclusion, we have studied the interaction between a nano-contact spin torque
oscillator and microwave currents of different frequencies and powers. We observe clear
frequency modulation up to frequencies as high as 3.2 GHz and both injection locking and
intermodulation at frequencies close to the STO operating frequency. While modulation
sidebands are well described by non-linear frequency and amplitude modulation theory, the
intermodulation phenomena do not seem to follow the expected classical dependence on
the injected power. It is possible that intermodulation is limited by the inertia of the STO
as it tries to follow the injected signal.
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 is gratefully acknowledged. J.Å. is a Royal Swedish Academy of Sciences
Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation.
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