Resonant magneto-acoustic switching: influence of Rayleigh wave frequency and wavevector

We show on in-plane magnetized thin films that magnetization can be switched efficiently by 180 degrees using large amplitude Rayleigh waves travelling along the hard or easy magnetic axis. Large characteristic filament-like domains are formed in the latter case. Micromagnetic simulations clearly confirm that this multi-domain configuration is compatible with a resonant precessional mechanism. The reversed domains are in both geometries several hundreds of \mu m^2, much larger than has been shown using spin transfer torque- or field-driven precessional switching. We show that surface acoustic waves can travel at least 1mm before addressing a given area, and can interfere to create magnetic stripes that can be positionned with a sub-micronic precision.

In this framework, we report on the optimum conditions for acoustic magnetization reversal, and also hint to its limits. For this study, we chose to work on a dilute magnetic semiconductor, (Ga,Mn)As, in which the carrier-mediated ferromagnetic phase exhibits magnetoelasticity. Although its Curie temperature remains well below room-temperature, the tunability of its magnetic properties has proven instrumental to demonstrate key concepts in spintronics [22,[25][26][27].
Here we present a study of the influence of the travelling/stationary SAW direction with respect to the magnetic easy axis and of the SAW frequency up to about 1GHz. We show how these govern the efficiency of the switching, but also the size and shape of the domains. In particular, homogeneous domains several hundreds of microns wide are obtained on in-plane magnetized (Ga,Mn)As, a substantial improvement over out-of-plane ). In the SAW-FMR regime, a small angle precession of the magnetization (black arrow) ensues, provided a hard-axis field is applied (blue arrow). (b) Schematics of the "split 44" design of the IDT. An rf pulse excites the transducer which generates a strain pulse. (c) Gated transmission S12 measured using a Vector Network Analyzer (T =20K, ksaw// [1][2][3][4][5][6][7][8][9][10]). . The acoustic power was 16mW for 5f0 and 7f0, 50mW for 3f0 and 85mW for f0 (the different powers reflect the frequency dependency of the excitation electronic circuit). Up to these powers, corresponding to a surface strain of εxx ≈ 10 −5 , we observe that the attenuation and velocity variations are power independent (linear regime). The inset is a schematics of the field-dependence of the precession frequency. The resonance field lies where fprec(B) is closest to the the first intersection with the SAW frequency (dotted lines). At the second crossing, the effective rf field generated by the SAW is almost zero [17]. (b) Acoustic attenuation variations calculated for a SAW propagating along [1][2][3][4][5][6][7][8][9][10] at f0, 3f0, 5f0 and 7f0 -same color coding as (a). (c) SAW attenuation variations at resonance, extracted from the data of (a) and the calculation of (b).
Since the zero-field precession frequency of the layer -a few GHz as estimated from the anisotropy constants measured by cavity ferromagnetic resonance (FMR) -was systematically larger than the SAW frequencies, a field was applied along the hard axis [110] using an air-cooled CAYLAR dipole to bring the magnetization precession frequency down into resonance with the SAW (inset of figure 2a).

SAW-FMR REGIME
Before using high amplitude SAWs to switch the magnetization in (Ga,Mn)As, we show that acoustic waves can excite FMR equally whether propagating along the hard or the easy magnetic axes. SAW-FMR shows up as a resonant attenuation of the wave amplitude or a resonant velocity change [17][18][19]31]. To measure them, the layer is first magnetized uniformly along the easy [1][2][3][4][5][6][7][8][9][10] axis and 400ns-long rf bursts are sent on the exciting IDT (1 or 2) at 1 kHz repetition frequency. The amplitude/phase of the transmitted pulse are then monitored with respect to the hard-axis field along [110] (see references 17 and 22 for a more detailed description of this time-domain SAW-FMR measurement procedure). Amplitude and phase variations were measured versus field at the four SAW frequencies for the two orthogonal travelling directions, and a large range of powers. For the sake of conciseness we will focus here on the low power 20K attenuation data (figure 2a), sufficient to convey our message. The amplitude and velocity variations measured at other temperatures and powers were quite similar qualitatively to the data shown in Refs. 17 and 22. A pronounced resonance is evident in figure 2a, as had already been seen in out-of-plane magnetized (Ga,Mn)(As,P) [17] or in-plane magnetized Nickel [19,31,32]: the SAW triggers small oscillations of the magnetization around its equilibrium position (schematics in figure  1a). Using the cavity-FMR determined anisotropy constants, we calculate f prec (B) (inset of figure 2a) and see that the experimental resonance field is around 40mT, for which the precession frequency stands closest to the SAW frequencies. The resonance is close to the saturation, where the f prec (B) curve has a steep tangent. This explains the weak variation of the experimental resonance position with f saw . Note that a 0.2 • misalignement of the field with respect to the [110] axis was taken in the calculation, which will be justified in the following.
The amplitude and position of the acoustic reso-nance are very similar for SAWs propagating along the hard or easy axis. This can be explained by computing the effective field generated by the SAW. In the reference frame of the equilibrium magnetization [17,19] The position of the static magnetization, ϕ 0 , is defined with respect to [1][2][3][4][5][6][7][8][9][10]. Here we have introduced the uniaxial and biaxial magnetostrictive coefficients A 2ε , A 4ε and A 2xy [28]: are the out-of-plane and in-plane uniaxial anisotropies, M S is the magnetization at saturation, and ε XX,0 , ε ZZ,0 and ε XY,0 are the static biaxial and shear strains (in the GaAs <100> axes frame). Because A 2xy A 4ε in this material [21,28], the A 4ε term in µ 0 h rf (t) is several thousand times smaller than the A 2xy term, so the absolute value of the tickle field has a very similar field dependence (via ϕ 0 (B)) for the two orthogonal SAW wave-vectors k saw // [1 ± 10].
Finally, the attenuation variations at resonance increase with the SAW frequency, from barely detectable at f 0 to over 15 dB.cm −1 at 7f 0 =990 MHz (figures 2a,c). This is a standard SAW FMR behavior since the absorbed acoustic power varies as P abs =- where χ is the magnetic susceptilibity tensor [19,32]. Using the semi-infinite model developed for (Ga,Mn)(As,P) in Ref. [17], we calculate the field-dependence of the SAW attenuation variations, assuming a SAW frequency dependent filling factor F (f saw )=0.78 h λsaw , a static shear strain ε XY,0 =2.10 −4 and a 0.2 • misalignement of the field with respect to the [110] axis (figure 2b). The shape and amplitude of the experimental SAW attenuation are well reproduced, as well as the frequency dependence of the attenuation at resonance (figure 2c). This strong dependence of the SAW attenuation with SAW frequency exists in both the linear and non-linear magnetization dynamics regimes, and will be critical for the switching efficiency.

SAW-INDUCED RESONANT SWITCHING
To observe the effect of a single SAW burst on the magnetization, a longitudinal Kerr microscope, sensitive to the [1-10] component of the magnetization, was used. More details on this set-up can be found in reference 33. Normalized Kerr images are taken as follows. The sample is first initialized magnetically + M 0 or − M 0 along the easy axis and a reference image taken. Applying a constant magnetic field along [110], a single SAW burst is then emitted (figure 3a), chosing its duration τ saw to ensure a plateau with constant strain wave amplitude (the rise/decay time of the acoustic burst is rather long -about 85ns -due to the transient passage of the wave through the excitation transducer digits, see figure 1b).
After bringing the field back to zero, a second Kerr image is taken, and divided by the reference one. The sample was reinitialized before any new SAW pulse was applied. Particular care was given to align the static bias field along the hard axis to impede domain nucleation, which could compete with the precessional reversal (hysteresis cycles are very square, with a coercive field of 2 mT at 20 K). Finally, as previously discussed and quantified in references [22,34] since no current is applied to the system, and thermoelasticity of GaAs is weak, no substantial temperature rise of the sample is expected from the passage of the SAW.

Influence of the SAW direction on the shape of switched domains
We first show data for a SAW burst travelling along the easy [1-10] axis after a + M 0 initialization. Figure  3b shows normalized images taken close to the exciting IDT 2 after a single 200ns-long burst (7f 0 =990 MHz, P exc =3.5W). This generated a surface strain component ε xx (z=0)≈2×10 −4 (see Appendix A for how the SAW power and amplitude are estimated from P exc -in the following we will drop the mention "z=0"). The reversal starts at low field, 12.5mT, and at the lower edge edge of the SAW wave-front where the displacement is higher due to the finite aperture of the transducer [35]. As the field is increased, the switching proceeds along filaments parallel to the SAW wave-vector. At 16mT and above, the magnetic pattern does not change anymore and is made of alternating + M 0 and − M 0 magnetized strips about 10-20µm wide, and several hundreds of microns long. The same experiment was then done with the SAW burst propagating along the hard magnetic axis [110] this time, parallel to the static bias field. Figure 3d shows images for the same SAW frequency as above, taken close to the exciting IDT 1, after a single SAW burst (P exc =1.5W). The estimated SAW amplitude is a little bit smaller than above, ε xx ≈7×10 −5 , so that switching starts at a slightly higher field, around 20 mT. The reversed domains have a very different shape. They now form patches or columns parallel to the wave-vector, with jagged edges. At 23mT, domains several hundreds of µm 2 have reversed on the SAW path.
In both configurations, the switching pattern does not depend on the SAW pulse duration, as long as it is longer than the transient regime. For shorter pulses, reversal persists in the (magnetically) weaker parts of the sample. It is observed at all temperatures up to T C at decreasing fields, as expected from the temperature dependence of the resonance [17]. No reversal was observed out of the SAW path, or when the IDT was excited out of its resonance. Monitoring the SAW amplitude versus field in both configurations shows that it now resonates lower than the 40  . This powerdependent downshift of the resonance had already been observed in out-of-plane magnetized (Ga,Mn)(As,P) [22] and is expected in the non-linear regime of magnetization precession, regardless of what drives it, be it an rf field [36] or spin transfer torque [37].
SAW switching also works after a − M 0 initialization (figures 3c,e). At low field, although the switched domains have the same overall shape, they are not located in the same region of the sample nor cover the same area as when starting from + M 0 (see the images at 13. To test the latter, we first do a control experiment where the magnetization is initialized + M 0 or -M 0 , the field ramped up to 40mT, and then brought back down to zero, without having applied any SAW pulse (figures 3b,c, "NO SAW" images). If the magnetization is brought fully along [110] under this field, we expect a collection of equiprobable + M 0 and -M 0 domains at remanence. The normalized images clearly show that this only occurs on one part of the image or another, depending on the initial magnetization, and that these regions correspond precisely to those switching under SAW. This could be well be explained by the existence of slightly curved field lines : if the sample is not exactly half-way between the coil poles, the field could be slightly offset to the right  4). Hence SAW-driven resonant switching is extremely sensitive to the precise alignment of the magnetic coil, as already shown experimentally and numerically on out-of-plane (Ga,Mn)(As,P) [22] Influence of the SAW frequency on the switching efficiency We now show how the efficiency of the switching varies with SAW frequency. This was quantified by averaging the switched area in front of the exciting transducer (dotted rectangle in figure 3d -20mT). Great care was taken to work at constant SAW amplitude, and constant magnetic field angle. We show for instance the resulting efficiency plot (figure 5) for k saw //[110], and a constant surface strain of ε xx ≈ 7 × 10 −5 . Reversal clearly occurs earlier in field with increasing SAW frequency. This  figure 3d). The rf excitation power is adjusted for a constant strain εxx(z=0)≈ 7 × 10 −5 . Switching at f0=141 MHz is too unefficient at this SAW amplitude to appear on this graph. The field was misaligned by a fraction of a degree, so that at high field, almost 100% of the area has switched.
is consistent with the increase of the SAW attenuation with f saw (shown in the linear regime in figure 2a, and similar behavior at high acoustic powers): the power is lost by the SAW to the magnetization, which fuels an efficient reversal. An identical behavior was found for k saw // [1][2][3][4][5][6][7][8][9][10].
Stationary SAWs: influence of fsaw on magnetic patterning period The data presented up to now has relied solely on propagating acoustic waves. Yet the use of stationary waves can be relevant for magnetic patterning, as was shown on FeGa by Li et al. [23] (f saw =158 MHz). The mechanism at work was not detailed in this paper, but probably implied the reduction of domain nucleation/propagation barriers [34] rather than precessional switching. Using the different available SAW frequencies of our device, we study the effect of f saw in resonant switching induced by stationary SAWs along [110]. For this, IDTs 1 and 1' are excited simultaneously and the magnetization is observed half-way between them (figure 6a). The applied field was chosen high enough to have larges patches of homogeneously reversed magnetization. Figures 6b-d show a close-up of the center of the sample after a single 400ns-long burst on each transducer at f 0 , 3f 0 and 5f 0 . For each of those frequencies, the stationary SAW clearly imprinted a λ saw /2-periodic pattern to the switched magnetization. This can be explained as follows: for two counter-propagating SAWs of amplitude A and relative phase φ, the stationary wave has an amplitude of the form A 110 =2Acos(ω saw t + φ)cos( 2π λsaw x + φ 2 ). Because the SAW burst is much longer than a single period, switching occurs when the SAW amplitude reaches a particular threshold in absolute value [22], yielding the λ saw /2 periodicity of |A 110 | in the magnetic pattern (figures 6b-d). Note that the micron-resolution of our microscope prevented us from seeing the stationary pattern at 7f 0 ≈ 990 MHz (fringe width λ saw /4=0.7µm).
Likewise, magnetic fringes along [100] can be patterned by exciting simultaneously two perpendicular SAWs (IDTs 1 and 2, figure 6e). This time the amplitude of the stationary wave reads A 100 = 2Acos[ π λsaw (x+ y) − ω saw t + φ]cos[ π λsaw (x − y) + φ]. The λsaw √ 2 -periodicity along [100] expected from |A 100 | is evident in figure 6f. A SAW wavefront parallel to the easy axis ( k saw //[110]) is however clearly the more favorable configuration since the resulting magnetic pattern presents a weak magnetostatic cost, the charges being comfortably sent to the extremities of the fringes. This is less true when at least one of the travelling SAW wavefront is perpendicular to the easy axis as in figure 6f, where a slight horizontal smudging of the fringes can be seen along [1][2][3][4][5][6][7][8][9][10].
Finally, changing the relative phase of the exciting bursts, one can also impose the position of the magnetic pattern. This was done for f 0 and 3f 0 (fringes parallel to [1][2][3][4][5][6][7][8][9][10]). The two bursts arriving on IDTs 1/1' have been delayed in steps of δφ=11.5 • using a mechanical phase-shifter. Before each of those steps, the sample was reinitialized + M 0 and a field applied along the hard axis. After switching for a given φ value, the intensity profile of the fringes along [110] was plotted, and the low-frequency background removed. A δφ-interpolated color map was then created with this data (figure 7). The λ saw /4 width of a single fringe clearly appears in this graph, as well as the λ saw /4 shift (half-period of the pattern) for a 180 • dephasing. An important consequence ensues from this experimental result: while resonant switching using stationary SAWs is probably not the most adapted to imprint very small magnetic patterns, the wave-like nature of the switching implies that a very precise, nanometric positionning of these patterns could easily be implemented, an appealing proprety for reconfigurable magnetic memories.

COMPATIBILITY OF MULTI-DOMAIN FORMATION WITH PRECESSIONNAL SWITCHING MECHANISM
Now that a clear experimental demonstration of SAWdriven switching of in-plane magnetization has been presented, we focus on the final multi-domain configuration that was obtained (figure 3), and whether it is compatible or not with a resonant switching mechanism.
In the simplified macrospin theory of precessional switching, when starting from a given initial magnetization ± M 0 , switching to ∓ M 0 should only be possible if the duration of the effective pulse field is an oddmultiple of half the precession frequency under the applied bias field [21]. This feature of precessional switching was beautifully demonstrated experimentally on small metallic devices (typically 100nm to 10µm-wide ellipses) for very short excitation pulses (electric [14] or magnetic fields [9], or current [11]). Beyond a few nanoseconds duration and for larger samples however, coherence was destroyed. Spatial and temporal dephasing of the precession was due to thermal effects (via the stochastic nature of the begining of the precession), or domain wall creation [4,6,11,38] (for bigger structures), rather than chaotic magnetization trajectories [10]. This lead to the switched/unswitched probability rapidly converging towards 50% with excitation pulse duration. We expect similar phenomena to occur when driving precessional switching acoustically, with the dephasing caused both by the spread in anisotropy constants in the magnetic layer and the relatively long duration of the excitation pulses.
Elegant analytical solutions have been derived for field and STT-driven precessional reversal of spin valves or magnetic tunnel junctions [39][40][41][42]. In order to keep calculations tractable, they are however often limited to idealized ellipsoid geometries. Being moreover macrospin calculations, they do not take into account exchange interaction and dynamic demagnetizing effects, which are expected to have a central role in the final switched domain configuration of our system. We therefore implement instead micromagnetic MuMax 3 simulations [43]. We first assumed no dispersion of the native uniaxial anisotropy constant K 2|| . The effect of the propagating SAW on the system is modelled as: K 2|| (x, t)=K 2|| + ∆K 2|| cos(k saw x − ωt) (see Appendix B for technical details on the simulations, and figure 8a-top for snapshots of the anisotropy). ∆K 2|| is proportional to the SAW amplitude and to the magneto-elastic coefficient A 2xy . Starting from a uniform + M 0 configuration, we apply a 20 mT magnetic field along the hard axis. Figure  8a-bottom shows selected snapshots of the time evolution of the magnetization (see the full "M(t) no dispersion.avi" movie in the supplementary information). As expected from macrospin calculations [21], the magnetization follows a wide angle precession around the vertical (hard axis) direction. Once the SAW emission is stopped (t=12.12ns), the acoustic pulse finishes propagating across the simulation window, and the magnetization returns to a small damped precession around its final equilibrium position. For τ saw =12T saw , the final state after removal of the field is a fully switched uni- form magnetization − M 0 , even though exchange and demagnetization energy costs have been taken into account. Moreover, for this magnetic field/SAW amplitude combination guarantying large amplitude oscillations of M( r, t), the final state can be chosen by how many multiples of T saw have elapsed during τ saw (figure 9a). The remanent state depends quite subtly on the detuning between the SAW frequency and the precession frequency [22].
When 1% fluctuations are included in the magnetoelastic constants, a very different behavior is observed (figures 8b,c and full "M(t) dispersion-SAW along easy/hard axis.avi " movies in the supplementary information). After a few SAW periods, the precession amplitude starts to vary across the SAW wavefront, introducing a progressive dephasing that is amplified as the SAW progresses. The spatial variations of the magneto-elastic constants reflect on the local efficiency of the SAW rf field. This triggers the nucleation of pockets of anomalies, which the SAW propagation then streches out into characteristic filaments. When the field is switched off (t=17 ns), exchange and magnetostatic energies govern the formation of clear micron-sized fully switched (blue) or unswitched (red) domains. The system has limited the formation of charged transverse domain walls along [110], preferring [44] the less costly Néel walls along [1][2][3][4][5][6][7][8][9][10]. This results in filamentation along the the easy axis. Varying the SAW pulse duration changes only weakly the final state (figure 9b), contrary to the case when no anisotropy fluctuations are included. The exact same simulation can be run with k saw ||[110] (figure 8c). In that case, the final domains are larger and less filamented than for the k saw || [1][2][3][4][5][6][7][8][9][10] case, since the SAW wave-front evolves parallel to the magnetic easy axis, a much more confortable situation from the point of view of magneto-statics.
We need to underline that the code implemented for the MuMax simulations imposes an identical spatial grid (here with a super-cell of 408nm) to describe the SAW propagation and the anisotropy fluctuations, so that large scale anisotropy fluctuations (e.g region size of a few microns) cannot be combined with a fine description of the SAW (e.g region size below λ saw /20). This is possibly why the characteristic micron-width of the filaments found in the simulation is smaller than the one observed experimentally (around 10-20µm). A full study of the critical dispersion scale to SAW wavelength ratio leading to filamentation is therefore out of the scope of the present paper. Yet, the simulations reproduce qualitatively very well three experimental features (figure 3): (i) the final state is not uniformly magnetized, but a collection of + M 0 and − M 0 domains. For k saw || [1][2][3][4][5][6][7][8][9][10], these take the form of filaments running roughly parallel to k saw , (ii) the final state is very weakly dependent on the SAW pulse duration, (iii) the switched domains are broader and less filamented when the SAW travels along the hard axis rather than along the easy axis. CONCLUSION We have presented a comprehensive investigation of resonant magnetic switching by a surface acoustic wave with a special emphasis on the role of the SAW frequency and the interplay between the SAW wavevector direction and the easy magnetic axis. The main results are the demonstration that : (i) Resonant reversal of in-plane magnetization is possible using large amplitude Rayleigh waves travelling along the easy or hard magnetic axis. The main difference between the two geometries lies in the aspect ratio of the reversed domains, with the magnetization clearly trying to reduce its magnetostatic energy by forming jagged or pointy domains along the easy axis. (ii) The reversed domains are several hundreds of µm 2 , much larger than previous demonstrations of STT-or field-driven precessional switching. This is also in stark contrast with SAW-induced switching in out-of-plane magnetized (Ga,Mn)(As,P) on which both the large spread of magnetic anisotropy and the natural tendency to self-organization into up/down domains meant that the switching occurred over small, sub-micron areas [22]. (iii) When the SAW wavefront lies parallel to the easy axis, the switched domains are large enough for periodic magnetic patterns to be carved out in stationary geometry, with a sub-micron positionning precision. There is no restriction to the minimum magnetic period that can be reached, save that of being able to excite high frequency SAWs (and to be able to observe submicron features). (iv) Micromagnetic simulations clearly confirm that the formation of multi-domains and the lack of pulse-length dependence of the final switched state are both compatible with a resonant precessional mechanism.
The limitations of this switching scheme have also been evidenced. The final pattern appeared very sensitive to field alignment and spatial variations of the anisotropy. This has also been one of the bottlenecks of precessional switching of MTJ or spin-valves, for which the asymmetry in the switching probabilites between parallel and anti-parallel configurations was due to the currentgenerated Oersted field or the stray field from the polarizing/analyzing layers [6,[45][46][47]. Several strategies were implemented in these systems to bypass this issue, such as the use of a synthetic antiferromagnet perpendicular polarizer to limit spurious stray fields. In the SAW switching scheme, a possible route would be to engineer the magnetic anisotropy to have the zero-field precession frequency close to f saw .
The long rise time of the SAW pulse -imposed by the large number of teeth required to excite efficiently the chosen frequency -is also likely detrimental to the determinism of the switching. The optimal design for SAW switching would therefore include a single digit-pair transducer (very short transient regime), with a SAW emission centered around a high frequency (high efficiency), and a uniaxial layer structured into sub-micron devices. This should allow to chose the final switched state whilst maintaining the advantages of propagating/stationary wave to adress selectivally a structure spatially.

A. Working at constant SAW amplitude
We have recently developed two precise techniques to estimate the SAW amplitude, using X-ray diffraction [48] or a vector network analyser [49]. The former is difficult to implement at cryogenic temperatures. The latter relies on measurements of the S parameters and modelling using the Coupling-of-Modes theory. It could however not be implemented here: (i) no "dip" was observed in the |S ii | 2 reflection coefficients, and (ii) working at cryogenic temperatures made it quite complicated to evaluate precisely the contribution of the fixtures, an indispensable step in this approach. For this reason, we proceeded to a gross estimate of the acoustic power as follows. Exciting IDT i with an rf voltage of amplitude U exc , we detect an echo of amplitude U det on the opposite transducer i'. The incident electrical power P exc is first measured on a matched load (50 Ω). The echo amplitude is then measured on a 50 Ω load and converted to an electrical power P det . Assuming an equal transduction coefficient β for both IDTs, we get P det = β 2 P exc , from which β is computed. Finally, the acoustic power is estimated as P saw =βP exc . The expression of the Poynting vector then yields the numerical value of the strain [35]. Note that this was performed at low temperature and in zero field (i.e far from any magnetic resonance capable of damping the SAW amplitude, see figure 2a). For the device presented here, the transduction insertion loss amounted to -25dB to -30dB, depending on the frequency, the IDT and the temperature.

B. Micromagnetic simulations parameters
The size of the simulation is 6533×6533×50nm (L x × L y × L z ) with 512×512×4 cells. Periodic boundary conditions are applied in the direction perpendicular to k saw . The following magnetic parameters were used: M s = 50 kA.m −1 , Gilbert damping α=0.1, K 2⊥ = -8133 J.m −3 ,K 2|| =800 J.m −3 , exchange constant [50] A ex = 10 −13 J.m −1 , cubic anisotropy K c =300 J.m −3 . Mu-Max on our OS does not accomodate two uniaxial anisotropies, so only the in-plane uniaxial anisotropy was considered. Discarding the out-of-plane anisotropy K 2⊥ effectively lowers the precession frequency and affects the in-plane and out-of-plane torques of the SAW on the magnetization. In this respect, quantitative comparisons between these simulations and the experiments should be made with great care. Acoustic parameters were taken as: f saw =990 MHz and V r =2852 m.s −1 , which yields λ saw =2.8 µm. Anisotropy fluctuations were implemented by dividing the simulation window into 16×16 regions of coordinates r i = (x i , y i ), in which small random anisotropy variations proportionnal to R could be added to the homogenous static anisotropies K 2|| and K c . Using those same 16×16 regions, the effect of the propagating SAW was modelled by adding a time-and space varying component ∆K 2|| ( r i , t) (see "Ku-dispersion.avi" movie in the supplementary material). Each region is 408nm≈ λsaw 7 wide, a satisfyingly small fraction of the SAW wavelength. For k saw along the easy axis, the final uniaxial anisotropy reads: K 2|| ( r i , t)=K 2|| (1+randNorm( r i )R)+ ∆K 2|| (1+randNorm( r i )R)cos(k saw x i − ωt)H(t − t 0 + xi Vr )H(−(t − t 0 − xi Vr − τ saw ), with ∆K 2|| =200 J.m −3 , τ saw = 10-12.5ns≈10-12.5T saw the SAW pulse duration, t 0 =100 ps, and R=0 or 0.01 depending on whether anisotropy fluctuations are taken into account or not. The field is turned off at t f =17ns, a few ns after the SAW has completely left the simulation window. The simulation is then run for an extra 4ns, i.e over twice typical damping times in this material [50].