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Frequency modulation of spin torque oscillator pairs
Ye. Pogoryelov,1, a) P. K. Muduli,1 S. Bonetti,1 Fred Mancoff,2 and Johan A˚kerman1, 3
1)Materials Physics, Royal Institute of Technology, Electrum 229, 164 40 Kista, Sweden
2)Everspin Technologies, Inc., 1300 N. Alma School Road, Chandler, Arizona 85224, USA
3)Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden
(Dated: 15 July 2010)
The current controlled modulation of nano-contact based spin torque oscillator (STO) pairs is studied in both the non-
synchronized and synchronized states. In the non-synchronized state the modulation sidebands are not well described
by theory, which indicates strong dynamic interactions between STOs. However, the synchronized state shows a well
behaved modulation and demonstrates robust mutual locking even under strong modulation. The power distribution of
the modulation sidebands can be quantitatively described by assuming a single oscillator model. These findings are
promising for potential applications requiring the modulation of large STO arrays.
PACS numbers: 72.25.Ba, 75.75.+a, 75.20.−g, 85.75.−d
Spin Torque Oscillators (STOs) are attracting rapidly grow-
ing interest due to their potential use for future microwave and
memory (e.g., in hard drive read-heads or spin transfer based
magnetic random access memory) applications.1–3 The prin-
ciple of the STO operation is based on the transfer of spin
angular momentum from a spin polarized current to the local
magnetization of a thin magnetic layer.4,5 The effect is typ-
ically achieved in a nanoscale device (∼ 100 nm in lateral
size) in which a large current density (∼ 108 A/cm2) can gen-
erate a precession of the magnetization. This precession is
then detected by the oscillation of the giant magnetoresistance
(GMR) or tunneling magnetoresistance (TMR) of the device.
However, the low output power of the STOs still limits their
use in actual applications. A promising way to increase the
STO output power is the synchronization of separate nano-
contact STOs that share a common magnetic layer.6,7 Spin
waves generated beneath each nano-contact propagate in the
common layer and can phase-lock with each other leading to
a coherent summation of the individual amplitudes of each
STO signal.8–11 Furthermore, it is imperative to demonstrate
that the signal from several synchronized STOs can be modu-
lated without perturbing, or even unlocking, the synchronized
state. While the modulation of single nano-contact based
STOs has been demonstrated13,14 and the literature on the
theoretical aspects of STO synchronization has been growing
steadily9–12,16–25, neither experimental nor theoretical studies
of modulated synchronized STOs have been presented.
In this work we study the current controlled modulation of
nano-contact based STO pairs in their non-synchronized and
synchronized states. In the non-synchronized state the indi-
vidual STOs are modulated independently and exhibit sepa-
rate sidebands that are not well modeled using prior modula-
tion theories. We ascribe this discrepancy to interactions be-
tween the STOs that exist even in the non-synchronized state.
However, the modulation of the synchronized state is well be-
haved and can be quantitatively explained assuming a single
STO model. Additionally, the robustness of the synchroniza-
tion, even under strong modulation, is encouraging for future
a)Electronic mail: yevgenp@kth.se
applications based on the modulation of large STO arrays.
The nano-contact based STO pairs studied in this work have
been described in detail in Ref. 7. The sputter-deposited film
consisted of a 5-nm-Pd/25-nm-Cu base electrode, a 20-nm-
Co81Fe19 fixed magnetic layer, a 6-nm-Cu spacer, a 4.5-nm-
Ni80Fe20 free magnetic layer, and a 2-nm-Cu/3.5-nm-Pd cap.
Point contacts were fabricated by electron beam lithography
followed by reactive ion etching through an SiO2 insulating
layer to the GMR film. The particular device studied in this
work has two point contacts, nominally 80 nm in diameter,
with 400 nm center-to-center separation (see schematic cross-
section in the inset in Fig. 1(a)).
The low frequency (100 MHz) modulating current is in-
jected from an RF source to the STO via a circulator. The dc
bias current is fed to the device by a precision current source
(Keithley 6221) through a 0-40 GHz bias tee connected in
parallel with the transmission line. The signal is then am-
plified using a broadband 16-40 GHz, +22 dB microwave am-
plifier, and finally detected by a spectrum analyzer (Rohde &
Schwarz FSU46). The actual RF current at the STO is cal-
culated by taking into account losses and reflections due to
impedance mismatch in the transmission line. For more de-
tails see Ref. 14. All measurements were performed in a mag-
netic field of 10 kOe applied at an angle of 66◦ to the film
plane to both maximize the output power26 and ensure that a
single, propagating, spin wave mode is excited.27–29
Fig. 1(a) shows the power spectral density (PSD) of the
STO signal as a function of drive current Idc. A clear tran-
sition from a non-synchronized two-signal regime to a single
synchronized state can be observed at about Idc = 54 mA,
where the total normalized power P/I2dc approximately dou-
bles from 43 nW/A2 to 91.1 nW/A2 [Fig. 1(b)], and the aver-
age linewidth drops significantly [Fig. 1(c)]. The doubling of
the total output power indicates that the amplitudes from the
individual nano-contacts add coherently, and in phase, and the
decrease in average linewidth is consistent with an increase in
the precessional mode volume, rendering thermal fluctuations
less effective in perturbing the precession orbit.6,7,30,31
For the modulation experiment below, we chose two oper-
ating points well within the non-synchronized (Idc = 51 mA)
and synchronized (Idc = 57 mA) regimes, respectively, indi-

223.5
24
24.5
25
Fr
eq
ue
nc
y
[G
Hz
]
(a)


Po
w
er
[d
B
ov
er
no
ise
]
0
5
10
15
20
25
Base electrode
CoFe − Fixed layer
Cu − Spacer
NiFe − Free layer
Cap
Point contacts SiO2
Top electrode
25
50
75
100
P/
I 2 d
c

[fW
m
A−
2 ] (b)
45 50 55 60
0
20
40
60
Idc [mA]
∆f


[M
Hz
]
(c)
FIG. 1. (Color online) Current dependence of the free-running nano-
contact STO pair: (a) Map of the peak power versus frequency and
applied current bias Idc. Peak power is expressed in dB over the
noise floor. Inset shows a schematic cross-section of the two nano-
contacts on a GMR spin-valve mesa. (b) Normalized integrated
power, P/I2dc and (c) linewidth versus Idc, where the data below the
synchronization transition (Idc < 54 mA) is given by blue triangles
and squares for the lower and higher frequency peaks respectively,
and within the synchronized region (Idc > 54 mA) by red circles.
Vertical dashed lines indicate the two operating points, Idc = 51 and
57 mA, used to compare modulation in the non-synchronized and
synchronized states.
cated by dashed lines in Fig. 1(a). Modulation was studied up
to a maximum modulation current of Im = 3 mA to ensure
that the STO pair stays within a given state at all times during
modulation.
Fig. 2 shows the result of current modulation. The free-
running STO spectra [Fig. 2(a)] develop a number of side-
bands equally spaced around each carrier signal [Fig. 2(b)]. In
the non-synchronized state, it is possible to identify all side-
bands as belonging to either the low-frequency carrier (“A”)
or the high-frequency carrier (“B”) and there appears to be
little interaction between any of the peaks. In the synchro-
nized state, the sidebands look remarkably similar to what one
would expect from a single STO and there is no indication of
any unlocking of the STOs under modulation. This is further
emphasized by plotting color maps of the resulting PSD as a
function of Im [Fig. 2(c) and (d)]. In particular, the synchro-
nized state shows very sharp and well formed sidebands at all
investigated modulation currents and is hence entirely stable
under modulation.
Fig. 3 shows the integrated output power of the carrier
0
5
10
15
20
25
Po
w
er
[d
B]
(a)I
m
= 0 mA
A
B
0
5
10
15
20
Po
w
er
[d
B]
(b)I
m
= 1.5 mA
A
A A A
AB
B
B
B
B
0
1
2
I m


[m
A]
(c)
Idc= 51 mA
23.6 23.9 24.2 24.5 24.8 25.1
0
1
2
Frequency [GHz]
I m


[m
A]
(d)
Idc= 57 mA
FIG. 2. (Color online) (a) PSD of the free-running STO for Idc =
51 mA (red) and 57 mA (blue); (b) Same spectra when a modulating
current (Im = 1.5 mA, fm = 100 MHz) is added. “A” and “B” denote
the individual STO signals in the non-synchronized state. (c) and (d)
show color maps of the PSD vs. Im in the non-synchronized and
synchronized states, respectively. Color scale is identical to Fig. 1(a).
(black triangles) and the first order upper (blue squares) and
lower (red circles) sidebands. Fig. 3(a) and (b) shows data for
the non-synchronized regime where there is a substantial dif-
ference in the sidebands of peak “B”, indicating rather strong
non-linearities for this STO. In the synchronized regime, on
the other hand, the first-order sideband amplitudes are found
to be nearly equal, suggesting that this non-linearity has been
suppressed. In fact, a highly linear behavior of f (Idc) in the
synchronized state (shown in the inset of Fig. 3(c)) possibly
suggests that the non-linearities of the individual STOs can
be averaged out once they synchronize. The amplitude mod-
ulation is also found to be negligible for the first-order side-
bands. However, when analyzing higher order sidebands, for
which amplitude modulation should have a stronger impact,15
we indeed observed a measurable difference (not shown),
consistent with the observed amplitude nonlinearity around
Idc = 57 mA [Fig. 1(b)].
Following the method developed in Ref. 14 we now use the
free-running STO characteristics [Fig. 1] to calculate the the-
oretically expected sidebands from a combined nonlinear fre-
quency and amplitude modulation (NFAM) theory14,15 with-
out any free parameters. In the synchronized state [Fig. 3(c)],
we essentially find perfect agreement between experiment
and calculations, which further corroborates that two syn-
chronized STOs behave as a single STO under modulation.
In the non-synchronized state, on the other hand, experi-

30 1 2 3
0
10
20
30
Po
w
er
[p
W
] (a)Idc= 51 mA
Peak A
0 1 2 3
(b)Idc= 51 mA
Peak B
0 1 2 3
0
50
100
150
200
250
300
I
m
[mA]
Po
w
er
[p
W
]
(c)
Idc= 57 mA
−3 −2 −1 0 1 2 3
24.4
24.6
24.8
∆I
m
[mA]
f
[G
Hz
]
FIG. 3. (Color online) Integrated power of the carrier (black trian-
gles) and the first order upper (blue squares) and lower (red circles)
sidebands for (a) Peak A and (b) Peak B for Idc = 51 mA and (c) for
Idc = 57 mA. Solid lines represent the corresponding calculated in-
tegrated power from NFAM theory. Inset in (c) shows the frequency
of the free-running nano-contact STO pair around Idc = 57 mA and
a corresponding 2nd order polynomial fit in solid red line.
ment and calculations show much less convincing agreement
[Fig. 3(a) and (b)]. We ascribe this discrepancy to strong in-
teraction between the two nano-contact STOs even in the non-
synchronized state. It is quite possible that dynamic effects32
of the modulating current may alter this interaction in a non-
trivial way and render the free-running (static drive current)
characteristics unrepresentative in describing the modulated
situation (dynamic drive current). Such a complex dynamic
dependence cannot be well modeled using NFAM theory.
In conclusion, we have studied frequency modulation of
nano-contact based spin torque oscillator pairs. In the non-
synchronized state, the individual STOs are modulated sepa-
rately and exhibit a more complex sideband behavior, which
we ascribe to interaction between the two nano-contact STOs
even in the non-synchronized state. At the same time the
synchronized state of nano-contact STOs demonstrates out-
standing stability under strong modulation. In addition, the
modulated response of synchronized STOs shows remark-
able agreement with NFAM theory derived for single STOs.
Synchronized STOs can consequently both be modulated and
modeled in a straightforward way as they behave as ordinary
single RF oscillators at the investigated modulation frequency.
We believe these results are important for the continued devel-
opment of communication and signal processing applications
based on spin torque oscillators.
Support from the Swedish Foundation for Strategic Re-
search (SSF), the Swedish Research Council (VR), the Go¨ran
Gustafsson Foundation and the Knut and Alice Wallenberg
Foundation is gratefully acknowledged. Johan A˚kerman is a
Royal Swedish Academy of Sciences Research Fellow sup-
ported by a grant from the Knut and Alice Wallenberg Foun-
dation. We thank Randy K. Dumas for critical reading of the
manuscript.
1P. M. Braganca, B. A. Gurney, B. A. Wilson, J. A. Katine, S. Maat, and
J. R. Childress, Nanotechnology, 21, 235202 (2010).
2J. A. Katine and E. E. Fullerton, J. Magn. Magn. Mater., 320, 1217 (2008).
3T. J. Silva and W. H. Rippard, J. Magn. Magn. Mater., 320, 1260 (2008).
4J. C. Slonczewski, J. Magn. Magn. Mater., 159, 1 (1996).
5L. Berger, Phys. Rev. B, 54, 9353 (1996).
6S. Kaka, M. R. Pufall, W. H. Rippard, T. J. Silva, S. E. Russek, and J. A.
Katine, Nature, 437, 389 (2005).
7F. B. Mancoff, N. D. Rizzo, B. N. Engel, and S. Tehrani, Nature, 437, 393
(2005).
8M. R. Pufall, W. H. Rippard, S. E. Russek, S. Kaka, and J. A. Katine, Phys.
Rev. Lett., 97, 087206 (2006).
9A. N. Slavin and V. S. Tiberkevich, Phys. Rev. B, 74, 104401 (2006).
10S. M. Rezende, F. M. de Aguiar, R. L. Rodrı´guez-Sua´rez, and A. Azevedo,
Phys. Rev. Lett., 98, 087202 (2007).
11X. Chen and R. H. Victora, Phys. Rev. B, 79, 180402 (2009).
12A. N. Slavin and V. S. Tiberkevich, Phys. Rev. B, 72, 092407 (2005).
13M. R. Pufall, W. H. Rippard, S. Kaka, T. J. Silva, and S. E. Russek, Appl.
Phys. Lett., 86, 082506 (2005).
14P. K. Muduli, Y. Pogoryelov, S. Bonetti, G. Consolo, F. Mancoff, and
J. A˚kerman, Phys. Rev. B, 81, 140408(R) (2010).
15G. Consolo, V. Puliafito, G. Finocchio, L. Lopez Diaz, R. Zivieri, L. Gio-
vannini, F. Nizzoli, G. Valenti, and B. Azzerboni, IEEE Trans. Magn.
(2010).
16J. Grollier, V. Cros, and A. Fert, Phys. Rev. B, 73, 060409(R) (2006).
17V. Tiberkevich, A. Slavin, E. Bankowski, and G. Gerhart, Appl. Phys.
Lett., 95, 262505 (2009).
18R. Bonin, G. Bertotti, C. Serpico, I. D. Mayergoyz, and M. D’Aquino, Eur.
Phys. J. B, 68, 221 (2009).
19E. Sano, Jpn. J. Appl. Phys., 46, L1123 (2007).
20B. Georges, J. Grollier, V. Cros, and A. Fert, Appl. Phys. Lett., 92, 232504
(2008).
21Y. Zhou, J. Persson, and J. A˚kerman, J. Appl. Phys., 101, 09A510 (2007).
22J. Persson, Y. Zhou, and J. A˚kerman, J. Appl. Phys., 101, 09A503 (2007).
23Y. Zhou, J. Persson, S. Bonetti, and J. A˚kerman, Appl. Phys. Lett., 92,
092505 (2008).
24Y. Zhou, S. Bonetti, J. Persson, and J. A˚kerman, IEEE Trans. Magn., 45,
2421 (2009).
25Y. Zhou and J. A˚kerman, Appl. Phys. Lett., 94, 112503 (2009).
26S. Bonetti, P. Muduli, F. Mancoff, and J. A˚kerman, Appl. Phys. Lett., 94,
102507 (2009).
27J. C. Slonczewski, J. Magn. Magn. Mater., 195, 261 (1999).
28A. Slavin and V. Tiberkevich, Phys. Rev. Lett., 95, 237201 (2005).
29S. Bonetti, V. S. Tiberkevich, G. Consolo, G. Finocchio, P. Muduli, F. Man-
coff, A. N. Slavin, and J. A˚kerman, submitted to Phys. Rev. Lett. (2009).
30S. E. Russek, S. Kaka, W. H. Rippard, M. R. Pufall, and T. J. Silva, Phys.
Rev. B, 71, 104425 (2005).
31T. J. Silva and M. W. Keller, IEEE Trans. Magn. (2010).
32Y. Zhou, V. Tiberkevich, G. Consolo, E. Iacocca, A. Slavin, and
J. A˚kerman, Phys. Rev. B, accepted (2010).