Phase locking of vortex based spin transfer oscillators to a microwave current

Abstract

Phase locking experiments on vortex based spin transfer oscillators with an external microwave current are performed. We present clear evidence of phase locking, frequency pulling, as well as fractional synchronization in this system, with a minimum peak linewidth of only 3 kHz in the locked state. We find that locking ranges of the order of 1/3 of the oscillator frequency are easily achievable because of the large tunability $\partial f/\partial I_{dc}$ observed in our vortex based systems. Such large locking ranges allow us to demonstrate the simultaneous phase locking of two independent oscillators connected in series with the external source.

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Phase locking of vortex based spin transfer oscillators to a microwave current
A. Dussaux,1A. V. Khvalkovskiy,1,2J. Grollier,1V. Cros,1A. Fukushima,3
M. Konoto,3H. Kubota,3K. Yakushiji,3S. Yuasa,3K. Ando,3and A. Fert1
1Unit´ e Mixte de Physique CNRS/Thales and Universit´ e Paris Sud 11, 1 ave A. Fresnel, 91767 Palaiseau, France
2A.M. Prokhorov General Physics Institute of RAS, Vavilova str. 38, 119991 Moscow, Russia
3National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
(Dated: September 22, 2010)
Phase locking experiments on vortex based spin transfer oscillators with an external microwave
current are performed. We present clear evidence of phase locking, frequency pulling, as well as
fractional synchronization in this system, with a minimum peak linewidth of only 3 kHz in the
locked state. We find that locking ranges of the order of 1/3 of the oscillator frequency are easily
achievable because of the large tunability ∂f/∂Idcobserved in our vortex based systems. Such large
locking ranges allow us to demonstrate the simultaneous phase locking of two independent oscillators
connected in series with the external source.
Injection of a direct electrical current through spin-
valve structures or magnetic tunnel junctions offers the
possibility to induce microwave steady-state magnetiza-
tion precession by the action of the spin transfer torque.
Due to the magneto-resistive effects, these oscillations
are converted to an a.c. electrical signal at microwave
frequencies [1, 2]. Such spin transfer nano-oscillators are
advantageous for applications in wireless telecommuni-
cations, but despite significant progress in increasing the
power of these oscillators and reducing the linewidth [3],
these parameters however do not yet match requirements
for practical applications. Synchronization of many os-
cillators is a solution to overcome these issues [4, 5]. One
of the mechanisms of synchronization of many oscilla-
tors discussed in Ref. [6, 7] is based on their ability to
adapt their frequency to the frequency of an injected a.c.
current. Synchronization of a single oscillator to a mi-
crowave source has been demonstrated experimentally for
systems in which the motion of a quasi-uniform magneti-
zation has been excited [8, 9]. In our work, we study syn-
chronization to a microwave current of oscillators having
a vortex in the free layer of a magnetic tunnel junction
(MTJ). We have demonstrated that these spin transfer
vortex oscillators (STVOs) result in large emitted power
with low linewidth compared to oscillators based on a
quasi-uniform magnetization precession[3]. We find that
such STVOs can be locked to the fractional frequencies
of the microwave current source as well as to its main
frequency. The ratio of the locking range to the emis-
sion frequency can be very large, and it allows us to ob-
serve experimentally the synchronization of two separate
STVOs to a common external microwave current.
In this letter, we perform phase-locking experiments
using STVOs made of circular shape nanopillars (diam-
eter D = 170 nm) from the same MTJ wafer as in Ref.
[3]. The magnetic stacks, grown by sputtering, are com-
posed of PtMn 15 / CoFe 2.5 / Ru 0.85 / CoFeB 3 /
MgO 1.075 / NiFe 15 / Ru 10 (nm). The ratio thickness
over diameter of the free NiFe layer is chosen in such a
way that a magnetic vortex is stabilized as a remanent
magnetic state. The top layer of the synthetic antiferro-
magnet (SAF) PtMn/CoFeB/Ru/CoFeB serves as a po-
FIG. 1: (a) Frequency, (b) integrated power, (c) linewidth
evolution of the emitted signal as a function of the applied
out-of-plane magnetic field for Idc = 3.5 mA. In the dotted
region, the magnetic vortex is excited by the spin transfer
torque.
larizer. The tunnel magnetoresistance (TMR) is 10 %.
Microwave emissions are recorded on a spectrum ana-
lyzer and injection locking experiments are performed by
adding a microwave circulator between the bias tee and
the sample, to inject a microwave current, Irf, from an
external source. In our convention, a positive current is
defined as electrons flowing from the NiFe magnetic layer
to the SAF.
As we demonstrated before [3], a rather large out-of-
plane magnetic field, H≈ 5.5 kOe, is needed in order to
tilt the polarizer magnetization and therefore to induce
a perpendicular component of the spin current, that is
required for the excitation of the vortex gyrotropic mo-
arXiv:1009.4076v1 [cond-mat.mtrl-sci] 21 Sep 2010

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FIG. 2: (a) Power spectrum map of the spin transfer vortex
oscillator with frequency fosc excited by a microwave current
Irf = 0.80 mA. The map is recorded at H = + 5.76 kOe, Idc=
3.5 mA. The source frequency fsource is swept from 450 MHz
to 1650 MHz (red line). The white dashed lines are guides
for the eyes showing 3/2 fsource and 2 fsource. (b) linewidth
of the signal emitted with an external a.c. current Irf = 0.80
mA swept from 1000 MHz to 1600 MHz. (c) locking range of
the single vortex based oscillator as a function of the external
a.c. current amplitude for H = + 5.76 kOe and Idc = 3.5
mA (red curve), linear fit obtained for Irf ≤ 0.25 mA (black
curve).
tion with a uniform polarizer [10]. In Fig. 1, we plot the
frequency (a), the power (b) and the linewidth (c) as a
function of the out-of-plane field H for Idc= 3.5 mA. For
H < 5.5 kOe, the out-of-plane spin current is too small to
excite vortex motion, thus only thermally excited vortex
resonance with low power and large linewidth is observed.
At very large field (H > 6.5 kOe), the magnetic config-
uration is no more a vortex but rather a quasi-uniform
magnetic state with low emitted power and very large
linewidth. The fields of interest for the present study go
from 5.5 to 6.5 kOe, in which spin transfer torque vortex
precession is present, along with large power (1.5 - 2.5
nW) and narrow linewidth (1 - 5 MHz). An important
feature in this field range is that the combined action
of the spin torque and the Oersted field leads to large
frequency tunability ∂f/∂Idc[3].
We then study the phase locking properties of our
STVO for an out-of-plane field H = + 5.76 kOe and
Idc= 3.5 mA, at which the oscillator frequency (corre-
sponding to the gyrotropic motion of the vortex core)
is fosc = 707 MHz, the linewidth is 4.7 MHz, and the
integrated power is 2.5 nW. In Fig.2 (a), we present a
map of the power density spectra recorded with Irf =
0.80 mA, as a function of the external r.f. current fre-
quency, fsource, varying from 450 MHz to 1700 MHz (the
red dotted line in Fig.2 (a) is the injected r.f. signal).
When fsourcecomes close to fosc, the oscillator first de-
viates from its natural frequency and eventually beats
exactly at the source frequency. The values of fsource
for which the STVO signal disappears, define the locking
range. The signal reappears when fsource is again well
separated from fosc. These behaviors are characteristic
of phase locking of a non linear oscillator to an exter-
nal signal. We observe additional peaks coming from
the modulation of the external rf current by the oscilla-
tor, as expected in microwave injection experiments (the
peak corresponding to fsource- foscbeing the most visi-
ble here [11]). Note that, in the locking regime, a direct
access to the signal spectral properties is impossible as
the peaks from STVO and the source merge [8, 9].
Interestingly, in addition to the synchronization at the
fundamental frequency, we also demonstrate that the os-
cillator is locked to the source when its frequency fsource
is equal to some fractions of fosc, for example fsource≈
3/2 foscand fsource≈ 2 fosc(dotted white lines in Fig.2
(a)).These effects are not related to the source non
linearity since no sub-harmonics are emitted. Because
of the large locking effects, the oscillator does not come
back to its free running frequency between the different
fractional synchronization regions. Most non-linear os-
cillators can exhibit such higher order synchronizations
when the driving force is large enough [12]. For the ex-
periments of synchronization to a microwave current of
quasi-uniform magnetization, the efficiency of the spin
transfer torque did not permit to see such effects [8, 9].
Urazhdin et al. have recently shown that for symmetry
reason, a microwave field strongly couples to the uni-
form mode allowing a large locking range and fractional
synchronization [13]. Here, we demonstrate that with a
vortex based oscillator, a microwave current turns out to
be an efficient driving force.
Besides its fundamental interest, the fractional syn-
chronization also allows us to investigate the character-
istics of the emitted signal due a locked STVO. In Fig.2
(b), we display the variation of the signal linewidth while
fsourcevaries from 1.0 GHz to 1.6 GHz. Both for fsource
around 2/3 foscand 2fosc, a strong reduction of the peak
linewidth of the locked STVO is observed down a mini-
mum value that is only due to the resolution bandwidth
(RBW = 470 kHz) used for this large frequency scan
measurements.We have performed additional measure-
ments at fsource = 2fosc with much lower RBW (0.91
kHz), allowing us to determine the intrinsic linewidth of
3 kHz. We attribute the increase of linewidth around
the regions of fractional synchronization to successive
locking-unlocking events occurring at the timescale of
the measurements, that broaden the signal. All the fea-
tures for the linewidth visible in Fig.2 (b), give us definite
proofs that we effectively observe phase locking of a vor-
tex gyrotropic motion to the microwave current delivered
by the external source. In particular, once locked, the

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small variation of the vortex oscillation frequency with
time, that has been identified as the main source of the
linewidth [14], is canceled.
We have also studied the evolution of the phase locking
with the amplitude of the external rf signal. In Fig.2 (c),
we plot the locking range at the fundamental frequency
i.e.fsource = fosc for Irf ranging from 0.025 mA to
0.80 mA. For small excitations (Irf≤ 0.25 mA), we find
that the locking range increases almost linearly with Irf
with a slope of 873 MHz/mA. In this regime of small
driving force, no fractional synchronization was observed.
For larger Irf, the coupling between the oscillator and
the source becomes strongly non linear thus explaining
the existence of fractional synchronization regimes. A
theoretical prediction of the locking range versus driving
force amplitude cannot be achieved without a model for
spin transfer induced vortex oscillations including non
linearity in the different forces.
FIG. 3: (a) Optical microscope image of two separated oscilla-
tors, labelled STVOs 1 and 2, that are electrically connected
in series by wire bonding. (b) Power spectra measured for
fsource = 1650 MHz (red dots) and without source (black
dots). In the latter case, the power has been multiplied by
a factor of 10. (c) Power spectrum map obtained for STVO
1 and 2, with frequencies fosc1 and fosc2, connected in series
recorded with H = + 5.82 kOe, Idc = 3.5 mA and sweeping
the source frequency fsource from 600 MHz to 1800 MHz with
a microwave current Irf = 0.67 mA. The white dashed lines
show the evolution of 3/2 fsource and 2 fsource.
In previous studies, the maximum locking range ob-
tained by microwave current injection in the quasi-
uniform magnetization regime, represented only a very
small fraction (about 1% ) of their free running frequency
[8, 9]. In contrast, we demonstrate here that the lock-
ing range with our STVO goes up to 250 MHz for Irf
= 0.80 mA, that is more than 35% of the oscillator gy-
rotropic frequency. Key parameters which define the os-
cillator ability to synchronize to an external signal are
the linewidth and the tunability, i.e. ∂f/∂Idc[8, 9]. For
this reason, the experiment presented in Fig.2 has been
performed at the field (5.76 kOe) which gives the highest
tunability to our STVO: 160 MHz/mA. This large value
is in striking contrast with the small tunabilities reported
on STVOs by other groups, typically a few 10 MHz/mA
[15–17]. In our system the spin transfer emissions occur
in a field range where the resonant frequency is strongly
affected by the external field (see supplementary infor-
mation in Ref. [3]). The out-of-plane field deforms the
vortex shape whereas torques due to spin transfer and
Oersted fields tend to push the magnetization back in-
plane, leading to strong frequency variations with cur-
rent. In contrast, for small fields (H < 5.5 kOe), the
tunability is less than 40 MHz/mA resulting in a small
locking range of about 40 MHz. In the field range of large
power spin transfer vortex precession of Fig. 1, the large
locking-range of 250 MHz results from the combination
of high tunability and small signal linewidth.
The large locking range of our STVOs and the small
frequency dispersion from sample to sample provide us
with the opportunity to demonstrate coherent oscilla-
tions of two independent oscillators locked to the source.
Subsequently, we connect by wire bonding two oscillators
in series, labeled STVO1 and STVO2, separated by a few
millimeters (see Fig.3 (a)). As expected, the emission
spectrum contains two independent peaks, correspond-
ing to the emission of each oscillator. The spectral max-
ima are at fosc1= 811 MHz and fosc2= 832 MHz, the
linewidths of the peaks are 7.0 MHz and 3.3 MHz, and
the integrated power are 0.6 nW and 1.0 nW respectively
(see black curve in Fig.3 (b)). We then study the locking
of these two STVOs to the source, for an external field
H = + 5.82 kOe, Idc= 3.5 mA by injecting, as before, a
microwave current Irfof 0.67 mA. In Fig. 3 (c), we show
the map of the power spectrum for this system with two
STVOs. We clearly observe for the two oscillators both
synchronization at the fundamental frequency as well as
fractional synchronization to the external source. When
the two locking ranges overlap, as for example, for 800
MHz < fsource < 860 MHz, both oscillators are phase
locked to the source, and emit in-phase. The regions of
synchronization to the second harmonic do also overlap,
allowing us to clearly demonstrate that the emission oc-
curs at a single frequency with a strong narrowing of the
peak (see red curve in Fig.3b at fsource= 1650 MHz).
In summary, we have demonstrated that a spin trans-
fer vortex oscillator can be locked to an external rf cur-
rent not only at its main frequency but also at fractional
frequencies such as 3/2foscor 2fosc. Inducing large tun-
abilities, ∂f/∂Idc, of the vortex gyrotropic mode by using
appropriate dc current and out of plane field values, we
achieve large locking ranges, of the order of the STVO fre-
quency. The observation of higher order synchronization
allows to study directly the power spectrum characteris-
tics of the locked STVOs, for which we find for example
a linewidth as low as 3 kHz. In addition, we have shown

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experimentally the coherent oscillations of two STVOs
connected in series synchronized to the external source.
Our results demonstrate that vortex based spin transfer
nano-oscillators are good candidates to achieve the syn-
chronization of a large array of oscillators through their
self-emitted microwave currents.
The authors acknowledge Y. Nagamine, H. Maehara
and K. Tsunekawa of CANON ANELVA for preparing
the MTJ films.
the ANR agency (VOICE PNANO-09-P231-36) and EU
grant (MASTER No. NMP-FP7-212257) is acknowl-
edged.A.V.K. is partially supported by the RFBR
(Grant No. 09-02-01423).
Financial support by the CNRS and
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