Acoustic-driven magnetic skyrmion motion

Magnetic skyrmions have great potential for developing novel spintronic devices. The electrical manipulation of skyrmions has mainly relied on current-induced spin-orbit torques. Recently, it was suggested that the skyrmions could be more efficiently manipulated by surface acoustic waves (SAWs), an elastic wave that can couple with magnetic moment via the magnetoelastic effect. Here, by designing on-chip piezoelectric transducers that produce propagating SAW pulses, we experimentally demonstrate the directional motion of Néel-type skyrmions in Ta/CoFeB/MgO/Ta multilayers. We find that the shear horizontal wave effectively drives the motion of skyrmions, whereas the elastic wave with longitudinal and shear vertical displacements (Rayleigh wave) cannot produce the motion of skyrmions. A longitudinal motion along the SAW propagation direction and a transverse motion due to topological charge are simultaneously observed and further confirmed by our micromagnetic simulations. This work demonstrates that acoustic waves could be another promising approach for manipulating skyrmions, which could offer new opportunities for ultra-low power skyrmionics.

Here, we demonstrate the SAW-driven motions of Néeltype magnetic skyrmions due to the strong magnetoelastic coupling in magnetic multilayers integrated with on-chip piezoelectric transducers.By controlling the relative orientation of acoustic wave propagation and crystal orientation of the piezoelectric materials, we generate both Rayleigh waves (with both shear vertical and longitudinal displacements) and shear horizontal (SH) waves (with only shear horizontal displacements) that can be applied to skyrmions at the same sample area.We find the Rayleigh wave can generate but not move the skyrmions due to its dominant vertical displacement (Fig. 1a), consistent with the previous report 37 .By contrast, the SH wave can efficiently move skyrmions as a result of the strong magnetoelastic coupling induced by the in-plane strain gradients.The observed directional motion shows a longitudinal component along the wave propagation direction, and a transverse component with the sign depending on the topological charges, in analogy to the skyrmion Hall effect 12,43 .These experimental observations are further confirmed by our micromagnetic simulations.Our results not only provide an efficient approach to drive the skyrmion motion by electric field-induced strain wave, but also demonstrates the SAW could serve as a versatile platform to explore the skyrmion dynamics.
The difference of the skyrmion motion driven by Rayleigh and SH waves can be captured by the micromagnetic simulations by considering magnetoelastic coupling, exchange coupling and DM interaction (see Method and Supplementary Information note 2 for detail).Figs.1b and 1e show the simulated spatial distribution of the out-of-plane normalized magnetization component mz, magnetoelastic energy density and total energy density for skyrmions that were driven by Rayleigh and SH waves, respectively.We find that the Rayleigh wave can only move skyrmions for less than half an acoustic wavelength (the skyrmions would then be trapped at the antinodes of the Rayleigh wave).The amplitude of the shear vertical displacement is usually much larger than that of the longitudinal displacement in a Rayleigh wave, in which the shear vertical displacement traps the skyrmions.The magnetoelastic energy density distribution of a skyrmion under a shear vertical wave shows a left-right asymmetry that is different from that under an SH wave including both left-right and up-down asymmetry due to the different displacement modes.The total energy density of the skyrmion (including the magnetoelastic energy density, anisotropy energy density, magnetostatic energy density, exchange and DM energy density) illustrates a symmetric distribution under a shear vertical wave, while an asymmetric distribution along the diagonal axis under an SH wave which causes the skyrmion to move towards the lower energy density direction.
We study the skyrmions driven by SAWs in Ta (5 nm)/Co20Fe60B20 (CoFeB, 1 nm)/MgO (1 nm)/Ta (2 nm) multilayers, because the multilayers show a weaker pinning effect than that in Pt/Co/Ta multilayers 10,20 , and the amorphous CoFeB has a strong magnetoelastic coupling and a low damping parameter, simultaneously 44 .The magnetic properties of the multilayers on a LiNbO3 substrate were characterized by a polar magneto-optic Kerr effect (MOKE) magnetometry (Supplementary Fig. S1a).The average diameter of skyrmions generated by magnetic field pulses in the sample is estimated to be around 1 μm (Supplementary Fig. S1c).The multilayers and interdigital transducers (IDTs) were integrated on a 64°Y-cut LiNbO3 piezoelectric substrate, as shown in Fig. 1h (optical image of the fabricated devices is shown in Supplementary Fig. S1d).By controlling the angle between the SAW propagation direction and the orientation of the piezoelectric substrate, the piezoelectric constant matrix can be transformed (see Supplementary Information Note 2), and thus the SH wave or Rayleigh wave can be generated independently with the wave propagation along the x or y direction, respectively (Fig. 1d).Fig. 1i shows a transmission spectrum (S21) between two IDTs using a vector network analyzer where the resonance frequencies of the SH wave mode and the Rayleigh wave mode are 486 MHz and 451 MHz, respectively.

Skyrmion generation by Rayleigh and SH waves
We first study skyrmion generation by using SAWs.Fig. 2 shows the MOKE images for the evolution of topological magnetic textures.At a zero magnetic field, magnetic textures are the maze domains (Fig. 2a).Then we start with a state with almost no magnetic texture by eliminating the initial maze domain structure (by the applied out-of-plane magnetic field of -0.8 mT), as shown in Fig. 2b.Magnetic skyrmions with a topological charge Q=+1 are created after exciting a propagating Rayleigh wave or SH wave with a pulse duration of 300 ms at the resonance frequencies, as shown in Figs.2c and  2d.The positive or negative sign of Q represents the center magnetization of the skyrmion being up or down.Figs.2e and  2f show the estimated skyrmion densities and sizes created by SH and Rayleigh waves as a function of applied RF powers.Note that the skyrmion density created by a Rayleigh wave is slightly smaller than that in the previous report 37 , because our pulse duration is smaller.We find that the SH wave can generate skyrmions much more efficiently than the Rayleigh wave when RF power is above 20 dBm.This indicates that the SH wave mode can couple with skyrmions more effectively because the SH wave with its dominant in-plane shear horizontal displacement produces stronger in-plane magnetoelastic energy.The average sizes of skyrmions generated by both SH and Rayleigh waves are estimated to be around 1 μm, similar to that generated by the magnetic field.

Skyrmion motion by SH waves
We then study the skyrmion motion by applying continuous SAW pulses with a fixed RF power of 26 dBm.Figs.3a-d (e-h) illustrate MOKE images of Q=+1 (Q=-1) skyrmion after exciting 1 st -4 th SH wave pulse with a duration of 300 ms (also see Supplementary movies 1 and 2).We find that the skyrmions move along the wave propagation direction (x axis) also with a transverse component (y axis), in analogy to the skyrmion Hall effect 12 .The motion distances d ( ) of the circled skyrmions (Q = ±1) are around 3 μm after each pulse.The SH wave with a wavelength of 10 μm also moves skyrmions (Supplementary Fig. S3).Statistically, 32% of the skyrmion population in the whole sample shows motion distance d>1 μm (Supplementary Fig. S4).The motion distances can be further improved by increasing RF powers or decreasing the wavelength of SAWs (Supplementary Fig. S4).In contrast, we do not observe any skyrmion motion driven by Rayleigh waves although the power of the receiving IDTs for a Rayleigh wave is 12 dBm higher than that of an SH wave (Supplementary Fig. S5), which is consistent with our micromagnetic simulations.
We estimate the skyrmion velocity driven by SH wave to be about 10 μm/s, which is similar to that driven by currentinduced spin-orbit torques with small current densities 43 .This could suggest that the skyrmion motion driven by SH waves under the current experimental condition remains in the creep regime.By progressively increasing the RF power, it is possible to increase the skyrmion velocity, but the wave amplitude is saturated (Supplementary Fig. S5).To transform from the creep regime to the flow regime with a much higher skyrmion velocity, one can use magnetic films with stronger magnetoelastic coupling constants and low damping parameters (Supplementary Information Note 3).
We summarize the motion trajectories (both dx and dy) of 18 different magnetic skyrmions in Fig. 4a.The skyrmions with Q=+1 (Q=-1) move consistently along the wave propagation direction with dy<0 (dy>0).This is in agreement with our micromagnetic simulation (Fig. 4b and 4c).The average deflection angles ( arctan( ) ) of Q=-1 and Q=+1 skyrmions are around 49.5°±15.2°and -34.2°±17.7°,respectively.The large variation of deflection angles is because the motion is influenced by the pinning potential induced by random defects.Our analytical calculation by solving the Thiele equation 46 reveals that the deflection angle is determined by the damping parameter and the ratio of effective magnetoelastic forces along the y and x axes (Fx/Fy).In Fig. 4d, the solid curves show the calculated deflection angle as a function of damping parameters with Fy/Fx = 0.3 (typical value for an SH wave).The calculated curves correspond to the experimental data (extract from Fig. 4a), which gives the damping parameters in the range of 0.01-0.07(the calculated deflection angles with different Fy/Fx are shown in Supplementary Fig. S6).The large deflection angles we observed in the creep regime are in sharp contrast with that observed in the current driven experiments (skyrmion Hall effect) 12 , as the skyrmion Hall angles are generally very small in the creep regime.This behavior indicates the magnetoelastic effective field can be an additional factor besides the topological Magnus force to determine the deflection angle.
We also find that decreasing the SH wave pulse duration causes the skyrmions to deform.When the duration of the SH wave pulse is reduced to 200 ms, some circular skyrmions deform into strips (see Supplementary Fig. S7).For longer SH wave pulses, more skyrmions are created and the average distance among skyrmions is reduce, causing a stronger skyrmion-skyrmion repulsion and a limited skyrmion motion (Supplementary Fig. S7).

Conclusions
In summary, we have experimentally demonstrated the motion of Néel-type skyrmions driven by acoustic waves in magnetic multilayers, in which the skyrmions can move along the wave propagation direction with a deflection angle with respect to the wave propagation direction, consistent with our simulations.This work provides insights into the understanding of magnetoelastic or magnetoelectric coupling in skyrmions.This approach of manipulating skyrmion dynamics by acoustic wave will potentially lead to skyrmion-based memory, logic and microwave devices with low power, without any current flowing in magnetic layers, in large sample areas, and with arbitrary motion trajectory (circular motion, Supplementary Fig. S8).The comparison of our work and other skyrmion-driven methods is listed in Supplementary Table.S1.The efficiency of acoustic wave driven skyrmion motion can be further enhanced by materials (with high magnetoelastic coupling) and device (with high power handling) engineering.More importantly, the motion trajectory with controlled directivity and high precision can be achieved possibly on a single skyrmion limit by using high-frequency acoustic waves (small wavelength) and techniques of acoustic wave manipulation, such as phased array acoustic transducers 47 .This is comparable to acoustic tweezers for dynamic microparticle manipulation 48 .

Methods
Sample fabrication.Synchronous two-ports SAW delay line devices were patterned on a 64°Y-cut LiNbO3 substrate by using photolithography and a liftoff fabrication process.Ti (5 nm)/Pt (150 nm) electrodes were deposited on a 64°Y-cut LiNbO3 substrate by using a high vacuum magnetron sputtering with Ar pressure of 3 mTorr.The SH type leaky SAW is confined on the surface using IDTs consisting of heavy metal Pt electrodes on top of the LiNbO3 substrate.The magnetic multilayers Ta (5 nm)/Co20Fe60B20 (1 nm)/MgO (1 nm)/Ta (2 nm) were sputtered by using high vacuum magnetron sputtering with an Ar pressure of 3 mTorr.P-MOKE measurements with in-situ RF voltages.The skyrmions were imaged by using a polar magneto-optic Kerr effect (p-MOKE) microscope, as shown in Supplementary Fig. S9.All measurements were performed at room temperature.The transmission spectrum between two IDTs was measured using a vector network analyzer (Keysight E5080B).Radiofrequency (RF) voltage pulses supplied to IDTs were provided by an analog signal generator (Keysight N5183B) and a function/arbitrary waveform generator (Keysight 33210A).The frequency of the RF voltage is the same as the resonance frequency of the SAW.SAW pulses are generated by an on-off keyed (OOK) RF modulation.
Micromagnetic simulations.The micromagnetic simulation is implemented including interfacial Dzyalosinskii-Moriya interaction, exchange interaction, magnetic anisotropy, magnetostatic, and magnetoelastic coupling contributions using MuMax3 [49][50][51] .Due to the limitation of the computational capacity, the length of the simulated layer is set as 256 nm, the width is 256 nm, and the height is 1 nm.The discretization cell size along the x, y, and z axes are 1 nm, 1 nm, and 0.5 nm, respectively.The material parameters used in the simulations are as follows: exchange parameter Aex = 1.8×10 −11 J/m, saturation magnetization Ms = 5.8×10 5 A/m, interfacial Dzyaloshinskii-Moriya interaction strength D = 3×10 −3 J/m 2 , perpendicular anisotropy parameter Ku = 6×10 5 J/m 3 , Gilbert damping parameter α = 0.2, a mass density of 8000 kg/m 3 , the first order and the second order magnetoelastic coupling constants B1 = B2 = -8.8×10 6 J/m 3 , elastic constants C11 = 283 GPa, C12 = 166 GPa, and C44 = 58 GPa 44 .The simulations are calculated under ideal conditions without considering elastic wave attenuation.However, the wave attenuation and the pinning effect due to the impurities and defects induced disorder in actual devices lead to skyrmion velocities driven by SAWs will be lower in reality.

Fig. 1 |
Fig. 1 | Concept of skyrmion motion driven by SAWs and the device schematics.a, Schematic diagram of skyrmion motion driven by a Rayleigh wave or a shear horizontal (SH) wave.b, Simulated skyrmion pinning under an elastic wave with periodic shear vertical displacements.The diameter of the simulated skyrmion is set to be 30 nm.The wavelength is 240 nm which is eight times as large as the simulated skyrmion size.The color scale represents the normalized (out-of-plane) magnetization component mz.c,d The magnetoelastic energy density (c) and the total energy density (d) of the skyrmion under an elastic wave with periodic shear vertical displacements.e, Simulated skyrmion motion driven by an SH wave.The arrow denotes the direction of the skyrmion motion trajectory.f,g The magnetoelastic energy density (f) and the total energy density (g) of the skyrmion under an SH wave.h, Schematic of the SAW delay lines configuration and the structure of the magnetic multilayer.i, Transmission spectrums (S21) of the SH and Rayleigh wave.The wavelength of SAWs is 8 μm.

Fig. 2 |
Fig. 2 | Generation of skyrmions by Rayleigh and SH waves.a-d, Polar MOKE images of the maze domain at a zero magnetic field (a), before exciting any SAW wave with an applied out-of-plane magnetic field Hoop=-0.8 mT (b), after exciting a propagating Rayleigh wave (c), and after exciting a propagating SH wave (d).The RF power is fixed at 26 dBm.The SAW pulse duration is 300 ms.The scale bar is 5 μm.e,f The density (e) and the size (f) of skyrmions created by SH waves and Rayleigh waves as a function of RF powers.

Fig. 3 |
Fig. 3 | Skyrmion motions driven by SH waves.a-h, The MOKE images of skyrmions motion for topological charge Q=+1 (a-d) and Q=-1 (e-h) skyrmions after the exciting of 1 st -4 th SH wave pulses.The red and blue circles highlight the position of the Q=+1 and Q=-1 skyrmions.The dotted circle in d and h represent the initial position of the skyrmions shown in a and e.The RF power is fixed at 26 dBm.The SAW pulse duration is 300 ms.The wavelength of SAWs is 8 μm.The SH wave propagating direction is from left to right.The SAW creates skyrmions with a topological charge Q=±1 when the positive or negative out-of-plane magnetic field (Hoop = ±0.8mT) is applied.The scale bar in the MOKE images is 2 μm.

Fig. 4 |
Fig. 4 | Skyrmion motion trajectories and skyrmion deflection angles driven by SH waves.a, Motion trajectories of magnetic skyrmions driven by SH waves in experiments.b,c Simulated skyrmions motion driven by the SH wave for Q=-1 skyrmions (b) and Q=+1 skyrmions (c).d, The experimental (blue and red regions) and numerically calculated (curves) skyrmion deflection angles (ϕsk) versus the damping parameter with a fixed ratio of effective magnetoelastic forces along y and x axes Fy/Fx =0.3.