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Large microwave generation from d.c. driven magnetic vortex
oscillators in magnetic tunnel junctions
A. Dussaux,1B. Georges,1J. Grollier,1V. Cros,1A. V. Khvalkovskiy,1,2 A. Fukushima,3M.
Konoto,3H. Kubota,3K. Yakushiji,3S. Yuasa,3K.A. Zvezdin,2, 4 K. 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
4Istituto P.M. s.r.l., via Cernaia 24, 10122 Torino, Italy
Abstract
Spin polarized current can excite the magnetization of a ferromagnet through the transfer of spin
angular momentum to the local spin system. This pure spin-related transport phenomena leads
to alluring possibilities for the achievement of a nanometer scale, CMOS compatible and tunable
microwave generator operating at low bias for future wireless communications. Microwave emission
generated by the persitent motion of magnetic vortices induced by spin transfer effect seems to
be a unique manner to reach appropriate spectral linewidth. However, in metallic systems, where
such vortex oscillations have been observed, the resulting microwave power is much too small.
Here we present experimental evidences of spin-transfer induced core vortex precessions in MgO-
based magnetic tunnel junctions with similar good spectral quality but an emitted power at least
one order of magnitude stronger. More importantly, unlike to others spin transfer excitations, the
thorough comparison between experimental results and models provide a clear textbook illustration
of the mechanisms of vortex precessions induced by spin transfer.
1
arXiv:1001.4933v1 [cond-mat.mtrl-sci] 27 Jan 2010
The spin transfer torque due to the interaction between a spin polarized current and a
magnetization [1, 2] has led in the last decade to the emergence of a number of interesting
novel effects such as current induced magnetization reversal [3, 4] or self-sustained magneti-
zation oscillations [5, 6]. The observation of spin transfer induced magnetization precession
brings some promising possibilities for designing a new type of nanoscale microwave oscil-
lators, the so-called spin transfer nano oscillators (STNOs), capable to compete in terms
of high frequency caracteristics with currently used millimeter-scale microwave synthetizer.
One of the tantalizing of the STNOs is that they are tunable over a wide frequency range by
varying the applied dc current or magnetic field. In most experiments up to now [5, 6], the
current-induced excitations were quasi uniform precessions in purely metallic structures,
which leads to a much too small generation of microwave power for the majority of ap-
plications. Various solutions have been recently proposed, for example by synchronizing
an assembly of STNOs [7–11] or by using MgO based Magnetic Tunnel Junctions (MTJs)
[12, 13] that deliver much larger power because of the larger magnetoresistance [14–16].
However the spectral linewidths with MgO MTJs are still very large (≈100 MHz) for stan-
dard excitations of the free layer in MTJs due to the chaotization of the magnetic system
induced by the spin transfer torque and/or the high non-linearity [17].
An alternative approach using the current driven motion of a magnetic vortex as source
of microwave power has been recently studied in metallic nanopillars [21]. A very interesting
mode is the circular motion of the vortex core around its equilibrium position [22]. This
low energy mode gives rise to very small linewidths (less than 1 MHz) in the sub-Gigahertz
range but generates only a very small integrated power in all metallic devices (about 0.01
nW). In the present paper, we show that large microwave powers and narrow linewidths can
be obtained simultaneously by spin transfer induced vortex motion in MgO MTJs.
The studied devices are circular shape nanopillars with a diameter d= 170 nm pat-
terned from the whole magnetic stack : synthetic antiferromagnet / MgO 1.075 nm/ NiFe
15 nm/capping. For the chosen parameters of NiFe thickness and dot diameter, we have
checked that the most favorable configuration is a single vortex state (see Methods). In
these nano-MTJs, the vortex dynamics is converted into a microwave signal thanks to the
large magnetoresistive ratio of the Tunnel Magnetoresistance effect (TMR). This enable us
to detect not only large sustained vortex oscillations induced by spin transfer but also low
signal associated to the ferromagnetic resonance of the thermally excited vortex. Such reso-
2
FIG. 1: (a) Power spectral densities (PSD) normalized by I2
dc, obtained for Idc = 2.6, 2.8, 3 and
3.2 mA with Hperp = 5.1 kOe. (b) Schematic of the different forces acting on the vortex core.
nant motion is efficient enough to produce competitive passive microwave elements such as
high gain resonators [18, 19].
In Fig.1 (a), we display some microwave emission spectra recorded with Hperp = + 5.1
kOe at several positive current values. For all Idc , a single peak is observed in the sub-GHz
frequency range that is characteristic of the coherent gyrotropic motion of the magnetic
vortex core induced by the spin transfer torque [21]. The emission frequency increases with
Idc (about 80 MHz/mA) together with a large increase of the peak power spectral density
(PSD). The best results have been obtained at large currents (Idc= 3.2 mA) but still below
the threshold above which the MTJ is damaged. At this value, the peak linewidth is only
1.1 MHz and the integrated power is about 5 nW. This is to our knowledge the highest
emitted power for STNOs showing similar linewidth. It therefore demonstrates the interest
to use the motion of a vortex as microwave source to benefit from the advantages of both the
coherency of the vortex gyrotropic motion and the large magnetoresistive signal provided
by a MTJ.
In most of cases, spin transfer excitations that is focused on the dynamics of a quasi
uniform magnetization, is suffering from a lack of comparison with theoretical predictions.
The reason comes mainly from the difficulties to accurately take into account the presence
of multi-modes, the different sources of spin transfer torques, the role of the Oersted field
or of the temperature [23]. An important impact of our work is that we provide a definite
comparison and an excellent agreement between experimental data, micromagnetic simula-
tions and theoretical predictions. As a matter of fact, we will show that our experiments can
3
be interpreted in the frame of the most recent theoretical descriptions of the spin-transfer
induced vortex gyrotropic motion using a modified Thiele equation [24, 25]. The starting
point is the modified Thiele equation taking into account the spin transfer torque :
G×dX
dt −∂W
∂X−ˆ
DdX
dt +FST = 0,(1)
where G=−2πpLMs/γezis the gyrovector, W(X) is the potential energy of the off-
centered vortex, ˆ
Dis the damping dyadic. In Fig.1 (b), we depict the four forces responsible
for the rotational motion of the vortex core around its equilibrium position. In Eq.(1), the
first two terms, corresponding respectively to the gyrotropic force and the restoring force,
are radial with respect to the vortex trajectory and their balance sets the frequency of the
motion. The last two terms, corresponding respectively to the viscous damping (that latter
on, we call Fα) and the spin transfer force FST are tangent to the trajectory, therefore their
compensation sets the amplitude of the orbit. Note that we introduce only the Slonczewski
term for the spin transfer torque since the Field like term is equivalent to an additional
applied magnetic field directed along the polarizer and its amplitude is negligeable compared
to Hperp we apply [26] . In the case of a fixed and uniform polarizer, we have derived an
expression for the spin transfer force FST given by [24] :
FST =σπJ pzMsLa~eχ,(2)
where σis the spin transfer efficiency equal to ~Pspin/2|e|LMswith Pspin the spin polar-
ization of the current, L the thickness of the dot, Jthe current density (defined as positive
for electrons flowing from the NiFe layer to SAF layers), athe orbit radius and ~eχthe unit
vector tangential to the orbit of the core. The spin transfer force FST is proportional to
pz, the out-of-plane component of the polarizer (pz=cosθ if θis the angle between the
magnetization and the out-of-plane direction). The expression of the damping force Fαis :
Fα=−2παη Ms
γωLap~eχ,(3)
where αis the damping constant, η=ˆ
D/αG is a damping parameter, Msthe saturation
magnetization of the NiFe layer, γthe gyromagnetic ratio and ωthe rotational speed. The
sign of the core velocity, and consequently the sign of Fαdepends on the polarity pof the
vortex core that can take two values : p= 1 for the core pointing up and p= -1 when it
points down.
4
The condition for sustained gyration of the vortex core is that the spin transfer force
counterbalances the damping. It follows from the respective signs of equations 2 and 3 that
spin-transfer induced vortex oscillations can be observed only if the vortex core and the
polarizer are pointing in the same direction when the current is positive, and if they point
in opposite directions when the current is negative. Our MgO based nanojunctions with a
vortex configuration are model systems compared to metallic devices to test these theoretical
predictions. The reasons are twofold. First the SAF structure of the polarizer provides a
uniform and fixed spin polarization. Second the current amplitude is small enough not to
bend the polarizer through the Oersted field or induce some dynamics into the SAF.
To show that, we plot in Fig.2 the integrated microwave power for Idc = 3.2 mA (top
panel)and the frequency for two values of Idc (bottom panel) as a function of the out-of-plane
magnetic field Hperp. The field is swept from -8.1 to 8.1 kOe and the out-of-plane component
of the polarization pzis expected to be proportional to |Hperp |.
Considering first the variation of the integrated power as a function of the out of plane
field in the top panel of Fig.2, we can identify the following successive zones. In zone I, for
Hperp <- 7.5 kOe, the absolute value of field is large enough to induce a uniform magnetic
configuration (no vortex) and the power is negligibly small. In zone II, a vortex turns out
and, as the vortex core polarity and the out-of-plane component of the polarization Hzare
both negative, a vortex gyration is induced and a large microwave power is emitted (about
5 nW at Idc = 3.2 mA). When |Hperp|becomes smaller than Hc≈4.5 kOe (zone III), the
out of plane polarization pzis too small to excite large gyrations and the power is negligible
at the scale of the figure. In zone IV, not only |pz|is too small for Hperp < Hcbut, with
the inversion of Hperp, the vortex core polarity and the polarizer have opposite signs. The
condition for vortex gyration is not satisfied and, even for Hperp > Hc, the power remains
very small (max. 270 pW at Idc = 3.2 mA). In zone V that begins at Hsw = 5 kOe, the
switching of the vortex core aligns pand pz, which induces gyrations and large microwave
power. Finally, in zone VI, for Hperp >6.5 kOe, as in zone I, there is no vortex and the
power is negligible.
The variation of the frequency as a function of the field in the bottom panel of Fig.2 fits
with the variation of the power discussed above. For |Hperp|>7.5 kOe (zones I and VI),
the magnetic field is strong enough to saturate the magnetization of the NiFe layer for all
Idc and a spatially uniform configuration with the magnetization pointing out-of-plane is
5
stabilized. The frequency of the excitations increases linearly with the field independently
on the current Idc, as expected for small amplitude uniform precessions from the FMR Kittel
formula. In this large field region, the slope is close to the expected value of 2.8 GHz/kOe and
the intercept with the zero-frequency axis occurs at 7.7 kOe, which corresponds to MN iF e
s
= 9 kOe after taking into account the demagnetizing factors. For |Hperp|between 6.5 and
7.5 kOe, one clearly sees in Fig.2 (a) a slight deviation from the Kittel mode, reflecting the
onset of a weak inhomogeneity that is suppressed when Idc increases. Such behavior is well
reproduced by the micromagnetic simulations of the frequency versus out-of-plane magnetic
field presented in Fig.3 by introducing a small tilt (1◦) of Hperp from the normal direction.
In both zone I and VI, as mentioned before, very low power emissions are measured in
agreement with what is generally observed for uniform magnetization oscillations of the free
layer.
The transition between the uniform magnetization and the vortex configurations (zone
II) occurs at Hperp = - 6.1 kOe (resp. transition from vortex to uniform configuration,
zone V, at Hperp = 6.1 kOe). It is characterized by a dip in frequency as can be seen
from the curve at Idc = 1 mA in Fig.2. This dip is well reproduced by the micromagnetic
simulations shown in Fig.3, and is related to a modification of the shape of the vortex
core that results into a softening of the mode. In this field range of large emission, the
simulations for Idc = 3.2 mA are in good agreement with the experimental results. We
find that the combined action of the spin transfer torque and the Oersted field strongly
modifies the evolution of the frequency and maintains the vortex present at larger Hperp (see
additional materials for the observation of the gradual disappearance of the frequency dip
as the current is increased). In the experiment and simulations, we see that several large-
amplitude non-uniform oscillating modes are successively excited when changing the field.
Note that such sequential transition of modes is not detectable by measuring the device
resistance versus field. Below the critical field |Hc|, only thermally excited vortex motion
associated with a very small power is observed and in consequence the two frequency curves
at different Idc are superimposed. While increasing Hperp from - 4.5 kOe to + 4.9 k0e, i.e.
zones III and IV, after a small increase of the frequency, the general trend is a decrease
of the gyrotropic frequency (see Fig.2, top panel) as already observed in vortex resonance
induced by ac field by De Loubens et al (see Eq.2 in Ref.[27]) due to the field dependence
of the vortex stiffness. The deviation from the expected linear behavior of the frequency vs.
6
FIG. 2: (top) integrated power as a function of the out-of-plane magnetic field. The field is swept
from negative to positive values. Hcis the critical field at which microwave oscillations occur for
Idc = 3.2 mA, Hsw is the field at which the vortex core reverses. (bottom) frequency as a function
of the out-of-plane magnetic field. Blue dots : Idc = 1 mA, red dots : Idc = 3.2 mA.
field is attributed to a deformation of the energy landscape by grains. For Hsw = + 5 kOe,
a large jump in frequency occurs due to the reversal of the vortex core polarity. After the
switching, it becomes aligned to the applied field and to the polarizer like in the case of large
negative fields (zone I). The reversal of the core polarity, associated with the abrupt change
in frequency and the recovery of the oscillations, is well reproduced in the simulation (see
Fig.3). It is worth emphasizing that a symmetrical behavior is obtained when saturating
first at large positive Hperp and then decreasing the field toward negative values.
As already mentioned, for negative currents, the condition to get large oscillations is
that the vortex core polarity and the out-of-plane component have opposite signs. The
measurement of the integrated microwave power for Idc = -5 mA as a function of Hperp,
7
FIG. 3: micromagnetic simulations of the frequency versus the out-of-plane magnetic field for Idc
= 1 and 3.2 mA. Different regimes are identified i.e out-of-plane uniform precession (STT-OOP),
spin transfer vortex oscillation (STT-VO) and thermally excited vortex resonance (Thermal VO).
swept from -8.1 to 8.1 kOe is presented as additional material. Large microwave power
is detected in a very narrow field window between Hc= 3.7 kOe and Hsw = 4.3 kOe. We
notice that Hsw is reduced in the case of negative currents because the vortex core velocity is
enhanced by spin transfer [28]. It implies that we have to increase the injected absolute value
of the current in order to decrease Hcand fulfill the condition Hc< Hsw. The counterpart
of this additional experimental verification of the model, is that we must use a dc current
that damages the junction quality leading to a decrease of the magnetoresistance ratio and
therefore a smaller microwave output power compared to the case of positive currents.
To extract some quantitative informations about the spin torque force, an expression of
the critical current density Jcfor the onset of sustained vortex oscillations can be obtained
by equalizing Eq. 2 and Eq.3. By this calculation, we predict that the ratio f /Jcbetween
the frequency and the critical current density should be proportional to the out-of-plane
polarization pz:
f
Jc
=1
8πγ~P
eLMN iF e
sαη pz,(4)
In our magnetic system, the spin polarization is coming from the CoFeB layer of the synthetic
antiferromagnet. Thus the evolution of pzwith the out-of-plane magnetic field can be
expressed by : pz=Hperp/MSAF
s. The ratio f /Jcis expected to vary linearly with Hperp.
In Fig.4, we plot the experimental values of f/Jcvs. the out-of-plane magnetic field for
8
FIG. 4: ratio of frequency over critical current density as a function of the out of plane magnetic
field for both sweep directions (red symbols : negative to positive, blue symbols : positive to
negative). The black lines correspond to the calculations using equation 4.
increasing (blue squares) and decreasing (red squares) values of the field. The expected
linear variation of f/Jcwith Hperp is clearly confirmed by the experiments. In Fig.4, we
also plot in plain lines the result from an analytical calculation using Eq. 4 taking MN iF e
s=
9.0 kOe, MSAF
s= 10.3 kOe, α= 0.01, η= 1.48 and Pspin = 0.53. We emphasize that this
value of Pspin is consistent with the MR ratios in conventional CoFeB/MgO/CoFeB MTJs
in which spin polarization Pspin = 0.5 - 0.6 for the CoFeB/MgO interface is found using the
simple Jullieres model. The excellent agreement between the experimental results and the
theoretical predictions on the whole field range reveals that not only a qualitative but also
a quantitative understanding of the spin transfer vortex dynamics has been achieved.
The location of the vortex core inside the nanodot can also strongly influence its dy-
namical properties. This core position can be controlled by the application on an in-plane
magnetic field Hin that forces the vortex to move perpendicularly to the field [29]. In ad-
dition, it provides a tool to investigate the role of the material grains on the motion of the
vortices but also potentially to increase the accessible frequencies. In Fig.5 (a), we display
the measurement of the gyrotropic mode frequency as a function of Hin. We observe an os-
cillating behavior of the frequency while the magnetic vortex is traveling from the center of
the dot where it nucleates, to the edge of the disk where it annihilates. Such large frequency
variations are due to the modification of the magnetization and/or the local anisotropies at
9
FIG. 5: (a) left axis (blue squares) frequency, right axis (green triangles) : integrated power as
a function of the in plane magnetic field .(b) Atomic Force Microscopy topography image of the
NiFe layer. Bottom : scan of the thickness as a function of the location.
the grain boundaries that changes the pinning potential [30–32]. From this measurement,
the number of material grains in the nanodot can be evaluated. We deduce a grain size of
about 40 nm in agreement with the AFM measurements shown in Fig.5 (b). Interestingly,
we find that when the resonance frequency is low (resp. high), the thermally induced vortex
fluctuations are enhanced (resp. reduced) as shown in Fig.5 (a); this is because the stiffness
of the potential well probed by the vortex core is reduced for lower frequency.
The perspective opened by our results is very promising. From the application point
of view, we have shown that the current-induced excitation of a vortex in a low resistivity
MTJ showing a MR ratio of only 10 %, can already lead to microwave emissions combining
large power (5 nW) and narrow linewidth (1 MHz). Furthermore the excellent fit between
our experiments and the theory makes our results turn out as a textbook example of the
physics of current-induced vortex gyrations. Interestingly, our work also indicates that
the observation of sustained vortex gyration at zero magnetic field, required for targeted
applications, is only possible either if an out-of-plane polarizer is used (as in this work by
applying an out of plane field) or if the polarizer is non-uniform or dynamically excited
[33, 34]. The quantitative agreement between our results and theory will also allow us to
define the best conditions, in terms of device structure (for example tilted or out-of-plane
polarizer) and materials parameters (lower R.A product and larger MR ratios), to improve
10
the efficiency of the spin transfer and the microwave power.
Methods :
The magnetic stacks grown by sputtering in a CANON ANELVA chamber contain a
synthetic antiferromagnet (SAF) and a free layer of NiFe separated by a thin MgO insulating
barrier : PtMn 15/ CoFe 2.5 / Ru 0.85 / CoFeB 3 / MgO 1.075 / NiFe 15 /Ru 10 (nm).
Details of the growth and fabrication process have been presented elsewhere [35]. The RA
product is 1.3 Ω.µm2for the parallel magnetization configuration. At room temperature,
the TMR ratio is 14 % under a bias current Idc of 1.6 mA. The topology of the top NiFe
layer has been investigated by means of Atomic Force Microscopy (see Fig.5 (b)). We find
that the surface roughness is mainly due a spacial distribution of the thickness of the poly-
crystal NiFe layer. Indeed, the surface of the underlying MgO layer was observed to be much
smoother than the NiFe layer.
Prior to the investigation of transport and microwave properties, a specific study has been
performed by high-resolution spin-SEM images (SEMPA) obtained at zero magnetic field
to characterize the actual magnetic structures on arrays of unconnected circular MTJs with
different diameters d(see Additional materials). For d= 72 nm, the remanent magnetic
state is a single-domain state for all the nanodots. By increasing the diameter to d= 125
nm, a few dots remain in single domain state whereas for most of them, the direction of
the magnetic moments is changing gradually in-plane leading to a contrast varying between
black and white. For larger diameters, the most favorable configuration is eventually a single
vortex state, in particular for the diameter of d= 170 nm chosen for this study.
The microwave response associated to the current induced vortex dynamics is studied by
applying the magnetic field Hperp out of plane and then by sweeping the dc current Idc from
0 to 3.2 mA. At each current value, microwave measurements up to 1.5 GHz are recorded on
a spectrum analyzer after 32 dB amplification. The background noise, measured at zero dc
current, is subtracted to the power spectra. In our convention, a positive current is defined
as electrons flowing from the NiFe magnetic layer to SAF layer.
For the micromagnetic simulations, we use our finite-difference micromagnetic code SPIN
PM. The simulated NiFe disk has a diameter of 170 nm, with a thickness of 15 nm. The
mesh cell size is set to 2 ×2×3.75 nm3. We took the following magnetic parameters:
α= 0.01 for the Gilbert damping, MN iF e
s= 9.0 kOe for the magnetization of the NiFe
layer, MSAF
s= 10.3 kOe for the effective magnetization of the polarizer (extracted from the
11
Additional figures :
FIG. 6: SEMPA images of circular 15 nm thick NiFe nanodots with different diameters d = 72,
125, 200 and 500 nm. For d = 72 nm, the remanent magnetic state is a single-domain state for all
the nanodots. By increasing the diameter to d = 125 nm, a few dots remain in single domain state
whereas for most of them, the direction of the magnetic moments is changing gradually in-plane
leading to a changing contrast between black and white. For larger diameters, the most favorable
configuration is eventually a single vortex state, in particular for the diameter of d = 170 nm chosen
for the rest of the study.
13
FIG. 7: frequency as a function of the out-of-plane magnetic field for Idc= 1, 1.6, 2.2, 2.6, and 3.2
mA. The field is swept from negative to positive values. The combined action of the spin transfer
torque and the Oersted field tends to force the magnetization of the vortex tail to remain in the
plane before the vortex is annihilated and therefore restrains the Kittle mode range to higher values
of the applied magnetic field.
FIG. 8: integrated power as a function of the out-of-plane magnetic field. The field is swept from
negative to positive values. Hc is the critical field at which microwave oscillations occur for Idc =
-5 mA, Hsw is the field at which the vortex core reverses.
Acknowledgments :
14
The authors acknowledge Y. Nagamine, H. Maehara and K. Tsunekawa of CANON
ANELVA for preparing the MTJ films. Financial support by the CNRS and the ANR agency
(NANOMASER PNANO-06-067-04, ALICANTE PNANO-06-064-03, VOICE PNANO-09-
P231-36) and EU grant MASTER No. NMP-FP7-212257 is acknowledged. B. G. is sup-
ported by a PhD grant from the DGA.
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