Acoustic control of magnetism toward energy-efficient applications

The manipulation of magnetism¹ is of great fundamental and technological importance for ultrafast, compact, and energy-efficient electronic and spintronic devices, e.g., high-capacity memories,² novel computing,³ and sensing devices.^4,5 The usual routes to control magnetism include the utilization of current-induced magnetic fields,^6,7 current-driven domain wall motion,⁸ voltage or electric field without flowing currents,^9,10 spin transfer torque,^11–15 spin orbital torque,^16–18 Dzyaloshinskii-Moriya interaction (DMI),¹⁹ linear or circularly polarized laser,^20–23 and static strain ²⁴ or dynamic strain ^25–27 due to the Villari effect.²⁸ Among them, strain-controlled magnetism ^29–31 has both theoretically and experimentally proven to be exceptionally energy-efficient and fast.^32–35 For instance, compared to current-induced domain wall motion, the energy dissipation of the strain-induced domain wall motion is several orders of magnitude smaller.^35,36 Static strain-induced changes in magnetization, magnetic anisotropy, and ferromagnetic resonance (FMR) have been intensively investigated in a wide range of multiferroic systems ^10,37–46 and tremendous progress has been made in understanding magnetoelastic coupling mechanism and improving coupling efficiency, which also has been timely reviewed.^47–53 However, dynamic strain-manipulated magnetism is somewhat unexplored.⁵⁴ Controlling and exploiting dynamic strain effects on magnetism is regarded as one of the highest priorities over the coming years,⁵³ driven by practical implications, e.g., ultrafast writing. In this review, we attempt to present important advances in dynamic strain- or acoustically controlled magnetization dynamics and switching in the past decade, from the viewpoint of both fundamental research and technological applications, as summarized in Fig. 1. We will discuss them in detail in the following sections.

Surface acoustic waves (SAWs)⁶⁷ act as an important means of carrying dynamic, elastic strain, which can propagate millimeter distances through magnetic materials (e.g., thin films or patterned nanostructures) and thereby trigger magnetization precession or even completely flip the magnetization. The review is organized in the following way. In Sec. II, we start with the underlying physics of magnetoelastic interaction from the magnetic free energy point of view, with a particular emphasis on the distinction between thermal excitation and SAW excitation. This is followed by a discussion of magnetoelastic simulations to model dynamic processes in the presence of these interactions. Then, we overview a variety of acoustic wave generation and magnetic detection schemes and list representative works of the acoustic control of magnetism in Table I in order to give the reader the best grasp of this field. We review the advances in the direct imaging of magneto-acoustic waves by combining photoemission electron microscopy (PEEM) with x-ray magnetic circular dichroism (XMCD), before discussing SAW-driven FMR, magnetoelastic coupling efficiency, selective excitation of localized magnetic modes, strong magnon-phonon coupling, and SAW magnetic field sensors. In Sec. III, we review acoustic spin pumping and potentially acoustic THz emitters. In Sec. IV, we present domain nucleation and precessional switching mechanisms, before reviewing SAW-assisted spin-transfer-torque (STT) switching. We point out the prospect of SAW-assisted all-optical-switching (AOS) based on recent experimental evidence and relevant theoretical prediction. In Sec. V, we review SAW-controlled magnetic textures, i.e., domain walls and skyrmions for racetrack memories. Section VI concludes the review with a discussion of future challenges and opportunities.

As an external magnetic field is applied to a magnetic material, its magnetic moments rotate to align with the field in order to minimize the overall energy of the system. This causes changes in dimensions of the magnet, which is known as magnetostriction effect. Its reciprocal effect, i.e., inverse magnetostriction effect or Villari effect, is that elastic strain (⁠$ε$⁠) in the magnet that can in turn affect the magnetization. In this section, we will discuss how a dynamic strain drives the magnetization based on inverse magnetostriction effect. First, the precessional motion of magnetization is governed by the Landau-Lifshitz-Gilbert (LLG) equation and affected by the competition of various free energy density terms⁶⁸ including the Zeeman energy (⁠$Fz$⁠), magnetocrystalline anisotropy energy (⁠$Fk$⁠), exchange coupling energy (⁠$Fex$⁠), and demagnetization energy (⁠$Fd$⁠), which directly contribute to the effective field $Heff$ in the LLG equation.^69,70

where $γ$ and $α$ are the gyromagnetic ratio and the Gilbert damping, respectively. In equilibrium, the magnetic moment is along $Heff$⁠, where the total magnetic energy density (⁠$F$⁠) is minimum. In the case of elastically driven magnetization dynamics, there is an additional energy term, the magnetoelastic energy (⁠$FMEL$⁠), which generates an internal magnetoelastic field (⁠$HMEL$⁠) contribution to the $Heff$⁠, acting as a driving force of the magnetization dynamics.^71,72

where $B1$⁠, $B2$ are the magnetoelastic constants, $Ms$ is the saturation magnetization, $Mi,j$ is the magnetization component, and $εii$⁠, $εij$ are the strain tensor components.

The intuitive effect of acoustic strains on the magnetization dynamics is exemplarily depicted in a Terfenol-D thin film,⁷³ as shown in Fig. 2(a). The competition of various energy densities results in four in-plane energy minima (1, 2, 3, and 4), which correspond to four preferred magnetization orientations in Fig. 2(b). However, after external tensile strain (⁠$ε>0$⁠; denoted as η in Ref. 73) or compressive strain (⁠$ε<0$⁠) is applied to the system, the minima of free energy are shifted by an angle of Δϕ, [Fig. 2(c)], which leads to the magnetization precessing toward a new minimum. As shown in Fig. 2(d), a steplike strain triggers the damped precession of the magnetization vector starting from the initial minimum 2 toward the new minimum 2′ (dashed line). In contrast, if the strain is a very short pulse, namely a rectangular one with a duration (⁠$τac$⁠) of 3 ps, which is far less than the precession period (⁠$Tprec$⁠) of ∼25 ps, the precession will damp back to the initial position 2 (solid line). The acoustic strain induces a magnetization rotation angle (⁠$Δθac$⁠) that is conjectured to be proportional to the acoustic pulse area, i.e., $∫η(t)dt$⁠, provided satisfying the condition $τac≪Tprec$⁠. Therefore, the $Δθac$ can be elevated by increasing strain amplitude and prolonging the pulse duration.

For the conventional electromagnetic wave (EMW)-excited magnetization dynamics, a time-varying magnetic “tickle” field perpendicular to an external, static magnetic field is independent of magnetization orientation. In contrast, the driving field H_MEL strongly depends on the magnetization and strain components per Eq. (5), which provides characteristic fingerprints of the SAW-driven magnetic dynamics.⁷⁴ For example, compared to the heat-pulse-triggered magnetization dynamics due to the ultrafast demagnetization, distinct results have been observed using the SAW excitation. In Fig. 3, the heat pulse quasi-instantaneously demagnetizes a Ni thin film [Fig. 3(a)] and a Ni nanomagnet [Fig. 3(b)], and within picoseconds the magnetization is restored and subsequently follows a damped sinusoid oscillation,^75–77 while the acoustic-wave-driven magnetization dynamics show an increase in the magnetic oscillation amplitude within the first nanosecond because it takes the time for the acoustic wave to travel to the nanomagnet⁷⁸ [Figs. 3(e)–3(f)]. It is worth noting that there is a slight lag between the magnetic system and the mechanical system, which has been confirmed by simultaneously imaging the evolution of both elastic strain and magnetization dynamics of nanostructures at the picosecond timescale using the stroboscopic x-ray microscopy.⁷⁹ In Fig. 3(g), the SAW-driven magnetization dynamics show a peak Fourier amplitude when the two systems are on resonance. The field-dependent magnetic precession frequencies observed in the heat pulse-triggered dynamics [Figs. 3(c)–3(d)] disappear.

In order to elucidate the underlying mechanism of optically generated SAW-driven magnetization dynamics, a multistep modeling approach was developed.⁸⁰ First, the temperature rise in nanostructures heated up by pump pulses is determined using the following three-temperature model^20,81–83 including electron (⁠$e$⁠), lattice (⁠$l$⁠), and spin (⁠$s$⁠) systems:

where $Ci$ and $Ti$ are the specific heat and the temperature of each system, $z$ is the distance into magnetic nanostructures, $gij$ is the coupling coefficient between two systems, $κ$ is the electron heat conductance, $ξ$ is the optical absorption depth, and $St$ is the absorbed laser fluence per unit of time.

In this model, the absorbed laser energy causes a rapid rise of the electron temperature $Te$⁠, while the lattice temperature $Tl$ remains low due to the much lower electron heat capacity. In ferromagnetic metals, after internal electron thermalization,⁸² the electron temperature $Te$ is nearly identical to the spin temperature $Ts$⁠. The subsequent relaxation process of hot electrons is dominated by the electron-phonon interaction, which leads to an increase in the lattice temperature $Tl$⁠. The three-temperature model can, therefore, be simplified to the two-temperature model:^82,84

The resulting thermal expansion and elastic motion are computed with time integration of the following equation ⁸⁵ via finite element method (FEM):

where $ui$ is the displacement, $ρ$ is the density, and $σji$ is the stress tensor. Figure 4(a) exemplary shows the displacement simulations with quasi-periodic boundary conditions (PBC) along the length direction of Al gratings that are used to launch acoustic waves toward a nanomagnet.⁵⁷ The displacement (⁠$ui,j$⁠) is then converted to the elastic strain (⁠$εij$⁠):

Finally, the magnetoelastic contribution H_MEL is calculated per Eq. (5), and fed into the Object Oriented Micromagnetic Framework (OOMMF)⁸⁶ micromagnetic simulations. The LLG equation is solved at each cell of nanostructures, where there is a temporal evolution of magnetization, which can be Fourier transformed into the frequency domain. In Fig. 4(b), the spatiotemporal profile of magnetization enables accurate parsing of the spatial character of SAW-driven FMR.

As described in Sec. II A, SAW-controlled magnetization dynamics is attributed to an effective variation in the magnetic free energy density. In order to thoroughly understand dynamic responses of magnetoelastic interaction, a stroboscopic X-ray microscopy-based technique has been developed to simultaneously provide an intuitive observation of both acoustic waves and magnetic modes with high spatiotemporal resolution (∼80 ps and ∼100 nm, respectively).⁷⁹ As shown in Fig. 5(a), photoemission electron microscopy (PEEM) and x-ray magnetic circular dichroism (XMCD)^87,88 were combined in the technique. The former offers electrical contrast of the SAW, whereas the latter provides the magnetic contrast. Both PEEM and XMCD images were synchronized with the SAW, which enables the establishment of a correlation between changes in local magnetization and strain field. By varying the SAW phase delay relative to the x-ray pulses, consecutive PEEM and XMCD images were recorded with phase intervals of 60° corresponding to 333 ps, as shown in Figs. 5(b) and 5(c), respectively. These images indicate that the four-domain Landau flux-closure state⁸⁹ evolves dynamically with the SAW propagation. It is worth noting that a pronounced phase delay of ∼48°, i.e., ∼270 ps is observed between the magnetic domain evolution (red curve) and the SAW (green curve) in Fig. 5(d), because the magnetization cannot follow the rapid change in anisotropy induced by the SAW. This must be considered in the magnetoelastic devices design. After the SAW incidence angle is rotated by 45°, the phase delay is reduced to about 90 ps in Fig. 5(e), approaching the experimental time resolution. In this experimental configuration, the SAW induces the same in-plane anisotropy in four domains that thus do not shrink or grow. Instead, the magnetization merely rotates coherently within each domain. In addition, the calculated dynamic magnetoelastic coupling coefficient is $2.2×106 Jm−3$⁠, comparable to the static one,⁸⁹ which suggests that the SAW can manipulate the magnetic state at the picosecond timescale as efficient as the static stain. Utilizing XMCD-PEEM microscopy, the SAW also has been observed to initiate a large-amplitude magneto-acoustic wave with the magnetization oscillation up to 25° over a long distance up to millimeters,⁵⁹ as shown in Fig. 5(f). In Figs. 5(g) and 5(h), the XMCD-PEEM images show the magnetic waves in a Ni film and the elastic strain wave in a LiNbO₃ substrate, respectively. Moreover, the amplitude of the magnetic wave linearly increases with increasing SAW amplitude. The effect of applied magnetic fields on the magnetic waves was also investigated. Figure 5(i) shows the magnetization reversal process in the presence of a magnetoelastic excitation. Here, an additional nonmagnetic Copper structure provides a zero-level reference of the magnetic contrast. In Figs. 5(j) and 5(k), the amplitude of the magnetic waves is strongly affected by applied magnetic fields and peaks at about 5 mT, where the external field is comparable to the uniaxial anisotropy field. In summary, this imaging technique provides a vivid observation of dynamic magnetoelastic response. Beyond this, it also can be used to study other dynamic strain-manipulated phenomena, such as nanoparticle manipulation⁹⁰ and tuning electrocatalytic activity.⁹¹ 

Acoustic waves can be generated by either electrical or optical methods. The electrical approach mainly refers to the interdigitated transducers (IDTs)⁹⁷ that consist of two sets of comb-like metallic electrodes (“fingers,” like Aluminum, Al) deposited on a piezoelectric^98,99 substrate, like lithium niobite (LiNbO₃) or quartz. When a radio frequency (rf) voltage signal is applied to the electrodes, it produces alternating regions of tensile and compressive strain between electrodes, i.e., a mechanical wave at the surface, due to piezoelectric effect. Ideally, the rf electrical signal (⁠$f$⁠) should be at the center frequency (⁠$f0$⁠) of the device in order to minimize insertion loss.¹⁰⁰ 

where $vs$ is the SAW velocity, and $p$ is the pitch between electrodes. In the experiment of SAW-driven magnetization dynamics, FMR is generally discerned via the measurement of SAW transmission using a Vector Network Analyzer (VNA). At the magnetoelastic resonance, the SAW transmission is strongly attenuated due to the increased absorption of acoustic energy, as shown in Fig. 6(a). On the other hand, several optical methods also have been employed to generate acoustic waves by optical excitation of acoustic Bragg mirrors,⁹³ metal thin films,^94,101,102 transient gratings,^95,103,104 periodic patterned nanostructures,^{56,78,80,105–107} or piezoelectric substrates,⁹⁶ as shown in Figs. 6(b)–6(f), respectively. In these experiments, the SAW-driven magnetization dynamics were measured by monitoring the Kerr rotation or the Faraday rotation. The acoustic strain amplitude varies dramatically in different experiments. A maximum strain amplitude generated by IDTs is of the order of 0.05%,¹⁰⁸ while a strain amplitude of <0.1% is obtained by laser-induced transient gratings.¹⁰⁹ A giant strain amplitude up to 1% has been observed in a hybrid Au/Co bilayer structure and an Al layer excited by an ultrashort laser pulse.^110–112 Moreover, the acoustic frequency extends to the THz range.¹¹² In Table I, a plethora of works are listed per different acoustic excitation and magnetic detection schemes.

Conclusive evidence of acoustically driven ferromagnetic resonance (FMR) was first observed in a ferromagnetic-ferroelectric (Ni/LiNbO₃) heterostructure via the measurement of SAW magneto-transmission.⁹² Unlike conventional FMR, SAW-driven FMR arises from the internal rf H_MEL rather than the external rf magnetic field, which makes it several orders of magnitude more efficient than the conventional FMR.¹²⁹ Moreover, the SAW-driven resonance exhibits a distinct magnetic field orientation dependence. For instance, the resonance can be switched “on” and “off” by a small field-angular rotation of about 0.1°, which indicates its potential for magnetic field sensing applications.¹²⁴ 

The SAW-driven FMR not only provides a different method to drive FMR, it also allows for an alternative analysis of magnetic material properties, such as the damping behavior. However, the damping constant extracted from SAW-FMR is almost ten times larger than that expected from cavity FMR measurements.²⁵ The reason is attributed to linewidth broadenings resulting from inhomogeneous excitation fields. In order to circumvent the inhomogeneous broadening effects, the SAW-driven FMR of periodic nanomagnet arrays of three different materials (Ni, Co, and TbFe) was thus performed.¹⁵⁹ The effective damping of these materials was successfully extracted and approached the intrinsic damping at high applied fields. However, at low fields, intrinsic properties of the materials were masked due to ensemble signals from multiple elements.¹⁵⁹ 

More recently, SAW-driven FMR has been detected from a single nanomagnet,⁷⁸ which enables one to determine the intrinsic damping of magnetic materials. Specifically, the complex Fourier amplitudes of SAW-driven FMR at the SAW frequency at all applied fields (⁠$Happ$⁠) around the resonant field (⁠$Hres$⁠) are considered in Fig. 7(a). The field dependent normalized real and imaginary parts of the Fourier amplitudes were fitted using the following Lorentzian functions:^78,159

to determine the pinning width (ΔH_p) in Fig. 7(b), which is directly related to the damping (⁠$αeff$⁠) and SAW frequency $fSAW$ via the following relation:^78,159

Note that the magnetoelastic coefficient does not appear in this relation. Here, we also compare the results from other techniques, like the time-resolved magneto-optical Kerr effect (TR-MOKE). In Fig. 7(c), the effective damping (α_eff) values extracted via SAW-FMR and TR-MOKE are summarized. For SAW-FMR, when four different SAW frequencies are used to excite the nanomagnet separately, the almost identical damping value is surprisingly obtained (blue triangle) and close to the intrinsic value determined from a fit^78,160 to the continuous film data (black circle). However, for the TR-MOKE, the extracted α_eff is field-dependent and only converges to the intrinsic damping at the high fields.¹⁶¹ The stark contrast indicates that the pure acoustic excitation without heating up the nanomagnet can be used to directly determine the intrinsic damping of a single nanostructure based on a single resonance. Later on, the effects of nanomagnet size and shape on the magnetic damping were systematically studied.^55,157 When the nanomagnet size is close to or larger than the SAW wavelength, the measured damping starts to deviate from the intrinsic value and shows a larger value as seen in Fig. 7(d), which is due to the inhomogeneous magnetoelastic excitation as confirmed by micromagnetic simulations.⁵⁵ Similarly, for an elliptic nanomagnet, the damping value measured via SAW-FMR is also much larger than the intrinsic value. This cannot be explained by the effect of shape anisotropy, which only results in a slight increase in the damping according to the following relation:¹⁶² 

where $Nxd$ and $Nyd$ are the demagnetization factors. Again, micromagnetic simulations¹⁵⁷ suggest that a spatial mismatch between natural magnetic modes and SAW-driven modes in the confined nanostructure plays a big role in the increase in damping. These findings of size- and shape-dependent damping provide important references for future “straintronic” devices.

In Sec. II D, we have discussed the effects of both nanomagnet size and shape on the measured damping via SAW-FMR. In this section, we will discuss the effects on the FMR amplitude. Nanomagnets with diameters (D) ranging from 730 to 150 nm were excited by various SAW wavelengths (λ_SAW).⁵⁵ The amplitude of the SAW-driven FMR increases by more than an order of magnitude as the nanomagnet size is reduced from 730 nm to 150 nm. In addition, the oscillation amplitude increases with SAW frequency when the size is below a critical value. The findings demonstrate that the efficiency of high-frequency, acoustically controlled devices scale favorably with device miniaturization.⁵⁵ The spatial character of the SAW-driven resonance is highly non-uniform in a large nanomagnet compared to a small one, which may account for the diminished amplitude and low efficiency of large nanomagnets [see simulations in Fig. 4(b)].⁵⁵ 

Apart from the reduction of nanomagnet size, the SAW-driven efficiency is also enhanced by focusing the SAWs.^56,163 In Fig. 8(a), an isolated Ni nanomagnet is surrounded by two sets of arc-shaped nanowires, which can focus the SAWs onto the nanomagnet [Fig. 8(b)]. As shown in Fig. 8(c), the amplitude of the SAW-driven magnetization oscillation is enhanced by a factor of ten compared to that generated by the heat pulse. In comparison to the normal SAW-driven case, the focused excitation raises the efficiency by four times due to the focused mechanical energy.¹⁶⁴ Therefore, the magneto-optical detection sensitivity^165,166 is pushed to the sub-100 nm range [Fig. 8(d)]. In Figs. 8(e)–8(h), by integrating multiple sets of nanowires with distinct space-to-space distances, SAWs with four different frequencies can be launched by a single pump beam and separately drive magnetization dynamics of four identical nanomagnets at different applied fields, which allows one to selectively excite a chosen element via simply tuning the field.⁵⁶ 

The magnon-phonon coupling has led to recent advances in new subfields,¹⁶⁷ like magnon spintronics^3,168 and spin caloritronics,¹⁶⁹ and continuing emergence of new phenomena including the spin Seebeck effect,¹⁷⁰ spin pumping,¹¹⁹ magnon-phonon conversion,¹⁷¹ and thermal Hall effect.^172,173 Consequently, the interaction between spin and lattice degrees of freedom has recently been the focus of increased research interest.⁵⁸ A fundamental question is how strong this interaction can be and, specifically, whether magnon-phonon coupling can be pushed into the strong coupling (SC) regime. SC is typically observed in photonic systems when the coupling strength between two fundamental excitations (e.g., exciton, photon) exceeds the decay rates of the individual systems. Recently, strong magnon-phonon coupling was observed in a couple of magnetic systems.^58,174 In contrast with the SAW-FMR (discussed in Secs. II D and II E) driven by the traveling SAWs located in the substrate, the strong magnon-phonon interaction is a direct coupling between magnetization precession and intrinsic mechanical vibrations of the element itself, which generates hybridized magnon-phonon modes. Here, the backaction of the magnetic resonance on the phonon system¹⁷⁵ must be taken into account. The phononic modes depend on the size, shape, and material properties of the element, as shown in the relation:⁵⁸ 

where $λ=Ev/1+v1−2v$ and $μ=E/(2(1+v))$⁠. $E$ and $v$ are the Young's Modulus and Poisson ratio, respectively. The magnetic precession modes can be described by the well-known Kittel formula:¹⁷⁶ 

The hybridized magnon-phonon modes can be governed by the following display:⁵⁸ 

When ω_C ≠ 0, the splitting of two modes occurs close to the region where two systems are degenerate, as shown in Fig. 9(b).

By varying the applied fields, the frequency of the magnons can be modified and brought into resonance with the phononic modes. The Fourier amplitude spectra [Fig. 9(c)] exhibit an avoided crossing,^178,179 which is in stark contrast with SAW-FMR presented in Sec. II D. Here, there are two peaks at each field value observed at and around the crossover field, which are the hybridization of the magnon and phonon modes.^171,180 To determine the strength of the magnon-phonon interaction, a dimensionless parameter, i.e., the cooperativity, is determined by the relation of $C=Γc2/κMκP$⁠, where $Γc$ is half of the mode splitting; $κM$ and $κP$ are the loss rate of the magnon and phonon system, respectively. When C is larger than 1, the coupling is in the strong coupling regime. C strongly depends on the in-plane orientation of the magnetization vector with the phononic vector. As shown in Fig. 9(d), the weighted coupling strength changes as the nanomagnet rotates in-plane and reaches the maximum at an angle of 45°, which corresponds with the cooperativity of ∼1.65. It means that the energy splitting of the hybridized modes can be tuned by various external degrees of freedom, which is especially desirable for the development of reconfigurable magnonic devices.^181,182 Very recently, the coupling strength has been significantly enhanced and achieved an unprecedented coupling strength of ∼8 in a Galfenol nanograting.¹⁷⁴ It was found that tuning the magnon mode to a quasi-transverse phonon mode led to a clear band splitting, suggesting strong hybridization, while tuning the magnon frequency to a quasi-longitudinal phonon mode did not lead to observable hybridization. Numerical simulations revealed that the strongest hybridization occurs when the spatial distributions of magnon and phonon modes overlap. In addition, a comparable mode strength between magnons and phonons is also necessary for strong hybridization. In summary, such strongly coupled magneto-mechanical systems may provide the possibility of developing more efficient transducers between magnonic and phononic systems.⁵⁸ 

It is well known that SAW devices^183,184 have been widely used as sensors for gases, pressure, temperature, humidity, etc. Recently, SAW-driven magnetoelastic coupling effect has been utilized to develop novel sensors for magnetic fields^64,184–186 that are pervasive in modern technologies such as electric current sensing, vehicle detection, biodetection, and so on. Relative to the existing spintronic magnetic sensors¹⁸⁷ based on magnetoresistance (MR) phenomena (i.e., Anisotropic MR, Giant MR, and Tunnel MR), strain-mediated devices possess higher energy efficiency and can be operated remotely.¹²⁴ For example, in recent work,¹²⁴ high-quality Fe thin films were epitaxially grown on GaAs substrates, and the SAW excitation was performed along the [110] direction with an external field (B_ext) applied at an angle ψ to [110], as shown in Fig. 10(a). Due to the highly oriented crystallinity trait, the films exhibit strong magnetic anisotropy. As shown in Fig. 10(b), the magnetic precession frequency (v₀) dramatically changes as B_ext is only tilted by 1° with respect to [110], which provides the prerequisite of the appealing applications. When B_ext is along [110], the minimum of the v₀ matches with the SAW frequency, which entails resonant magnetoelastic coupling. This can be observed in Figs. 10(c) and 10(d). SAW attenuation shows the highest peak at ψ = 0°, which represents the occurrence of resonant excitation. In contrast, when one rotates the field by even 0.1°, the attenuation peak value plunges by a factor of five. In addition, the variation of the field also results in the change of SAW velocity (V), which becomes steep around the resonant field. Most importantly, the highly sensitive angular dependence of the magnetoelastic interaction provides a large possibility for sensing applications. More magnetostrictive materials with a large anisotropy can be exploited in order to improve further the sensitivity and eventually outperform the existing spintronic magnetic sensors.

The research interest in spintronics has been growing very rapidly due to its practical applications in next-generation nano-electronic devices with low-power consumption and high memory and information processing capabilities.^188,189 The generation of spin currents, i.e., spin angular momentum flow, is regarded as one of most essential techniques required for the spintronic applications and can be implemented by means of nonlocal spin injection,¹⁹⁰ spin pumping,¹⁹¹ the spin-Hall effect,¹⁹² the spin Seebeck effect,¹⁹³ etc. Among them, spin pumping is an efficient pathway to generate spin currents that are pumped out of a ferromagnetic layer with precessing magnetization [M(t)] into a paramagnetic layer at FMR conditions,^188,194 as shown in Fig. 11(a). As discussed in Sec. II D, the magnetization precession of the ferromagnetic layer can be excited by acoustic waves, i.e., the SAW-FMR, which is analogous to the conventional FMR excited by electromagnetic waves, so one can expect to acoustically generate spin currents,¹⁹⁵ which indeed has been demonstrated in Co/Pt bilayers.¹²¹ Furthermore, the magnitude of acoustically generated spin current density is comparable to that generated by the common FMR.¹⁹⁶ 

In Fig. 11(b), SAWs are launched by applying a rf voltage to an input IDT. They then travel to a remote Co/Pt bilayer and excite the magnetization precession in a Co layer, which in turn emits a spin current (J_s) into a Pt layer.¹⁹⁷ The generated spin current can be converted to an electrical charge current to produce an electric field (E_ISHE) via the inverse spin hall effect (ISHE), as shown in Fig. 11(a). The E_ISHE is proportional to a voltage (V_DC) that can be measured to determine the strength of the generated spin current due to the relation:¹⁹⁸ 

where $DISHE$ is the ISHE efficiency, which can be strengthened by using noble metals such as Pt due to strong spin–orbit interaction and $σ$ is the spin polarization vector parallel to the magnetization direction in the magnetic thin film. The transmitted rf power (P_IDT) was detected by an output IDT. In Fig. 11(c), it is observed that the input IDT also launches an EMW that can be clearly distinguished from the SAW in the time domain. When a static magnetic field is tuned to the resonant fields (±4 mT), the changes in the transmitted SAW power (ΔP_IDT) are apparent compared to the non-resonant field of 30 mT (H_ref). The attenuated SAW power is attributed to the SAW-driven FMR. The SAW-driven spin pumping is also unambiguously discerned by recording the V_DC(t). At FMR conditions, a sign reversal of ΔV_DC is observed after the field direction is reversed in Fig. 11(d), which is considered to be characteristic behaviors of ISHE. Recently, the acoustic spin pumping was shown in the Ni/Cu(Ag)/Bi₂O₃ system¹²² due to the acoustically resonant excitation, where the generated spin current is efficiently transformed to charge current via the inverse Edelstein effect (IEE) due to spatial inversion asymmetry at the interface between two nonmagnetic layers.¹⁹⁹ In addition, acoustic spin pumping is also demonstrated in a magnetic insulator/noble metal (YIG/Pt) system at far below FMR frequencies (<10 MHz) in Figs. 11(e) and 11(f).^60,119,200 More intriguingly, an inverse phenomenon is observed. Acoustic waves are coupled with nonmagnetic metals based on spin rotation coupling^201,202 and thereby generate spin currents. For instance, in the NiFe (Py)/Cu system,¹²³ an alternating spin current is acoustically generated in the Cu layer and subsequently diffuses toward the interface of the bilayer system. The alternating spin current exerts an alternating spin torque onto the magnetization in the Py layer and consequently excites the FMR [Fig. 11(g)]. As shown in Fig. 11(h), a noticeable absorption of microwave power is observed in a Py/Cu structure. In stark contrast, the absorption is strongly suppressed in both Py and Py/SiO₂/Cu structures. Apart from the experimental progress, a linear-response theory²⁰³ has been presented that the strength of acoustic spin current is proportional to the acoustic power. Therefore, the spin current density may be improved by means of enhancing acoustic wave amplitude, e.g., using acoustic wave reflectors^204,205 and focusing acoustic waves.^164,206 Overall, from a fundamental point of view, acoustic spin pumping enriches spin mechanics,²⁰⁷ while from a technological point of view, it opens an intriguing perspective toward acoustic spintronics, where acoustic waves are exploited for developing novel spin-based devices.

Terahertz electromagnetic radiation in the frequency range of 0.3–30 THz is extremely useful for a wide range of applications, including basic research, imaging and spectroscopy, and so forth.²⁰⁸ Compared to ultraviolet, visible, and infrared lightwaves, the THz EMWs possess much weaker absorption in metals, semiconductors, and dielectrics, which makes THz emission spectroscopy especially applicable for studying relatively thick samples.⁶³ Despite the compelling applications, broadband, robust, and energy efficient THz sources remain elusive so far. Spintronic THz emitters, i.e., the combination of femtomagnetism and spintronics, provide a lot of prospects. Such THz emissions result from ultrafast demagnetization of magnetic metallic films,^209,210 helicity-dependent femtosecond photocurrents,²¹¹ or ISHE-generated charge current in a nonmagnetic layer adjacent to a ferromagnetic layer^208,212 and detected by free-space electrooptic sampling,²¹³ as shown in Fig. 12(a). In this section, we will focus on the THz emission originating from an ultrafast sub-picosecond or picosecond time-varying magnetization $M(t)$⁠, which is driven acoustically. In an ultrafast terahertz magnetometry⁶³ [Fig. 12(b)], in order to exclusively observe the transient demagnetization process and preclude the ultrafast ISHE effect on the emission, the Fe thin film was capped by a MgO layer instead of a metal layer such as Pd. Weak acoustic contributions to THz emission from laser-excited ferromagnetic Fe thin films⁶³ have been assigned to the pressure-induced changes in the length of magnetization vector. However, the extracted strain-induced magnetization changes appeared to be orders of magnitude higher as compared to tiny magnetization changes induced by static pressures in monatomic 3D ferromagnets.²¹⁴ In Fig. 12(c), the detected THz emission is reconstructed to the ultrafast magnetization dynamics that clearly include these two processes. Despite the dominance of the heat-driven demagnetization, the weak contribution from magnetoelastic interaction still opens a new pathway for THz emission in a heat-free and contact-free fashion. What's more, per acoustic spin pumping, an acoustic THz emitter may be envisioned as a magnetic heterostructure where femtosecond laser pulses–generated acoustic pulses excite magnetization precession and thereby inject a spin current into an adjacent nonmagnetic layer, which can be converted into a transient charge current to generate THz emission according to Maxwell's equations. Beyond magnetism, optically generated THz acoustic waves have been used to create the THz radiation at an interface between different piezoelectric coefficient materials.¹¹² In the future, a giant magnetostrictive material needs to be employed in order to achieve an efficient magnetoelastic THz-emitter that is comparable to its well-performing piezoelectric counterpart.

Surface acoustic waves have been demonstrated to selectively lower the coercivity and thereby assist magnetic reversal under a small applied magnetic field opposite to the initial magnetization. This generates magnetic patterns on a Galfenol film, as shown in Figs. 13(a)–13(d).¹³⁹ Moreover, the size of the pattern can be tuned by applied magnetic fields and acoustic energy. A 3-μm dot was successfully written on the thin film after the SAW while the wavelength of 20 μm was focused to a spot in Figs. 13(e)–13(f). The size of the dot can be further reduced by using shorter wavelengths.¹³⁹ Based on these findings, a novel paradigm in magnetic data recording has been proposed, where the write current is obviously lowered by increasing acoustic powers.^215,216 Later on, the mechanism behind the SAW-assisted magnetic switching due to the reduced coercivity was attributed to the SAW transiently lowering domain wall energy and thus assisting domain nucleation.¹¹⁵ A more efficient SAW-induced coercivity reduction up to 60% was observed in a diluted magnetic semiconductor, i.e., (Ga,Mn)(As,P).¹¹⁵ Compared to Galfenol, the magnetic semiconductor possesses low magnetic anisotropy and a weak exchange constant, which renders a small domain nucleation energy. However, the off-resonant domain nucleation process is relatively slow. For instance, SAW-triggered magnetization rotation from the easy axis to the hard axis of Co bars was shown to occur on time scales of 10 ns provided that the compressive, elastic strain arising from the SAW is above a threshold determined by the minimization of free energy.¹³³ On the contrary, resonant, precessional switching allows a sub-nanosecond magnetic reversal, which has been theoretically and experimentally demonstrated in the (Ga,Mn)(As,P) system.^108,114 When the SAWs initiate a large angle precession around an effective field, i.e., nonlinear spin dynamics,^217–220 the magnetization may end up switching completely if the excitation lasts for an odd multiple of half the precession period,²²¹ or if magnetic damping keeps the magnetization from “ringing.”²²² In fact, it is analogous to microwave-assisted magnetic recording (MAMR),^223–225 where a microwave field $h$ with the frequency close to the FMR frequency is used to excite a large-angle magnetization precession in the recording media, which significantly reduces the reversal field required in conventional magnetic recording.²²⁶ Mathematically, the precession amplitude can be simply characterized by the concept of cone angle, θ, between the effective field and the magnetization, which can be described as below in the nonlinear regime:²²⁷ 

where $H0$ is the resonant field at $h$ → 0, $M0$ is the saturation magnetization, and $ΔH0$ is the FMR linewidth. It has been theoretically predicted that the magnetization in a highly magnetostrictive material—Terfenol-D—can be reversed by a single acoustic pulse, ∼3 ps long.⁷³ Moreover, the precessional switching threshold depends on the product of the acoustic pulse amplitude by its duration, i.e., the acoustic pulse area. Recently, SAW-induced all-acoustic switching¹¹⁸ has been experimentally demonstrated in the absence of an external magnetic field, by engineering the precession frequency of a dilute magnetic semiconductor, (Ga,Mn)As to match the acoustic frequency at zero field. Moreover, toggle switching between two equilibrium magnetic states was achieved by ∼30 successive acoustic pulses. Most recently, ultrafast phononic switching of magnetic states has been achieved via resonant excitation of longitudinal optical phonon modes in yttrium iron garnet (YIG) thin films.²²⁸ In the future, the magnetoelastic interaction can be applied to the antiferromagnetic system. In summary, the magnetoelastic interaction-induced magnetization reversal provides an alternative approach to ultrafast magnetic recording without heating up the magnetic materials close to the Curie temperature.

Spin-transfer-torque (STT) technology has been applied to the magnetoresistive random access memory (MRAM) as a popular writing approach instead of using magnetic fields. In STT-MRAM, the information is encoded into the magnetic configuration of a nanoscale magnetic tunnel junctions (MTJ), where a charge current travels through a hard magnetic layer in the MTJ to polarize electrons that in turn exert a torque on a soft layer in the MTJ and thereby switch its magnetization. Although the STT offers the inherent advantage of all-electrical write and read over the use of magnetic fields, these STT-based MTJ devices operate at much higher energy dissipation than CMOS memory devices,^229,230 which may hinder the widespread applications of pure-current powered STT switching devices. SAW-assisted STT switching has been theoretically explored and proven a potential pathway to overcome the large write energy in the STT switching.^66,140,141 The underlying mechanism is that the SAW first induces a maximum deflection of magnetization and then the STT is applied to achieve complete switching, which reduces the STT current density required to switch the magnetization. The energy dissipation of SAW-assisted STT-MRAM can be reduced by an order of magnitude as opposed to the STT-MRAM alone in both in-plane MTJs¹⁴⁰ and out-of-plane MTJs.¹⁴¹ However, despite the promising results of theoretical modeling, to the best of our knowledge, conclusive, experimental evidence of SAW-assisted STT is still missing. Nevertheless, SAW-driven magnetization precession in the free layer of a MTJ has been observed, where the precession amplitude can either be increased or decreased by constructive interference or destructive interference of two time-delayed acoustic pulses, respectively.¹⁴⁶ Very recently, magnetoelastic coupling at an extremely high frequency (e.g., 60 GHz) was experimentally achieved in perpendicular magnetic [Co/Pd]_n multilayers¹⁴⁷ that are suitable for spintronic applications. Based on these experimental results, it should be very promising to experimentally implement SAW-assisted STT.

Since the discovery of all-optical switching (AOS) of the magnetization in GdFeCo alloys using a circularly polarized laser pulse about a decade ago,²² the high technological potential of AOS ^21,233–239 in magnetic recording has been quickly recognized owing to its record-breaking switching speed on the picosecond timescale. Subsequently, the research field was further boosted after observing the same effect in rare-earth-free magnetic multilayers^21,235 that have been heavily used in the field of spintronics. Until now, tremendous efforts have been made to disentangle the AOS mechanism.²³⁶ Nevertheless, to be technologically meaningful, the AOS must be more energy-efficient. To this end, spin transport-mediated AOS ^231,232,240 has been developed. In a magnetic spin-valve structure [(Co/Pt)₄/Cu/GdFeCo], a single laser pulse rapidly demagnetizes the ferrimagnetic GdFeCo layer, and thereby creates spin-polarized currents that flow through the metallic spacer Cu to the ferromagnetic (Co/Pt) layer, transferring the spin angular momentum via scattering between mobile and localized electrons. This eventually assists the optical switching in the ferromagnetic layer, as shown in Fig. 14(a). Instead of generating spin currents by means of ultrafast demagnetization, one can expect utilizing acoustic spin pumping as described in Sec. III A to launch spin currents from a reference layer to a free layer and either assist or hinder optical switching in the free layer depending on the relative orientation between two layers [Fig. 14(b)].²³² SAW-assisted AOS via the non-local transfer of spin angular momentum may reduce the threshold of the laser fluence significantly, which makes potential photonic memory devices²⁴¹ more energy-efficient. Other than energy efficiency, optically switched regions must be of nanoscale dimensions. In order to accomplish that, two-wire plasmonic gold antennas were placed on a TbFeCo thin film and thereby created localized enhancement of an optical field around the antennas. A ∼53 nm of AOS lateral size was resolved using an x-ray holographic imaging setup.²⁴² This size is comparable to that achieved by heat-assisted magnetic recording (HAMR). Alternatively, the recent experimental demonstration of focusing the SAW into a small region⁵⁶ (even <50 nm) may enable assistance with optical switching of a small lateral size based on SAW-induced localized spin angular momentum transfer from the reference layer to the free layer. This size may be even smaller than that achieved by the plasmonic antennas.²⁴² In fact, the previously described theoretical study⁷³ has revealed that the threshold fluence for AOS could be determined by the resulting acoustic pulse area, i.e., the product of acoustic pulse amplitude by its duration, suggesting the potential relation between the AOS and magnetoelastic interaction. Nevertheless, so far, there is still no direct experimental evidence validating the feasibility of SAW-assisted AOS, which needs to be addressed in the coming years.

The control of magnetic domain wall motion has great technological applications including magnetic domain-wall logic²⁴³ and racetrack memory² devices. Domain walls are typically moved using a magnetic field²⁴⁴ or a spin polarized current via spin-transfer or spin–orbit torques.^245–247 One of the major challenges in such studies is the large magnetic field or current density required to drive the system. Exploring energy-efficient and reliable ways of transporting a domain wall is a long-standing quest. Voltage-driven domain wall propagation in artificial multiferroic systems²⁴⁸ was expected to be a power-efficient approach but requires fabricating complex electrical contacts.²⁴⁹ In order to circumvent the fabrication complexity, using electrically generated SAWs to remotely manipulate a domain wall in a FeGaB nanowire was proposed [Fig. 15(a)].¹³⁷ Micromagnetic simulations [Fig. 15(b)] reveal that multiple domain walls can be synchronously displaced at velocities up to 50 m/s by detuning the SAW frequencies. To understand the physical mechanism underlying domain wall motion, a 1D semi-analytical model¹³⁸ was developed, which indicates that the primary role of the SAW is to drive oscillations of the azimuthal angle of the magnetization in the domain wall and thereby to drive oscillations of domain wall position through the demagnetizing field rather than to translate the domain wall directly. Indeed, recent experimental observations of SAW-assisted domain wall motion have been achieved in multilayered thin films,^136,250,251 and nanostrips.¹³⁵ Domain wall velocities are increased by an order of magnitude by a standing SAW compared to magnetic field alone.¹³⁶ Moreover, SAW-driven domain walls traverse preferentially toward antinodes and away from the nodes, and finally are pinned in the locations of SAW antinodes,²⁵¹ which could potentially enable domain walls to be more precisely manipulated by SAWs than by magnetic fields and currents. Further experimental work still needs to be done to optimize material properties and device designs so that the SAW-driven domain wall motion possesses speeds that are competitive with other approaches.

Similar to a magnetic domain, a magnetic skyrmion is a whirling topological spin texture in a magnetic material, where the spins rotate progressively with a fixed chirality from spin-up to spin-down, and then to spin-up again,²⁵² which is stabilized by Dzyaloshinskii-Moriya interactions (DMIs).^253,254 The size of the skyrmion can be as small as a few nanometers in diameter, akin to a “particle” that can be created, moved, and vanished, which makes it applicable for information storage and logic technologies²⁵² such as skyrmion racetrack memory^255,256 and skyrmion-based spin logic devices,²⁵⁷ provided that skyrmions can be excited and moved in an energy-efficient fashion. Electrical currents can initiate skyrmion creation and drive skyrmion motion, but require large current densities, which unavoidably creates issues with heat dissipation. To address the problem, electric fields^258,259 and thermal gradients²⁶⁰ are also used to generate and manipulate skyrmions. Very recently, a novel approach to create skyrmions by employing SAWs has been experimentally demonstrated in asymmetric Pt/Co/Ir multilayers,⁶¹ as shown in Fig. 16(a). In Fig. 16(b), the propagating SAW induces the skyrmion nucleation over a wide area of the magnetic film, and even after turning off the SAW, most of skyrmions still remain. Moreover, the density of nucleated skyrmions strongly depends on the acoustic power above a threshold power. Regarding underlying physical mechanism, micromagnetic simulations²⁶¹ reveal that spatially inhomogeneous effective torque resulting from magnetoelastic coupling and thermal fluctuations locally reverses the magnetization and thereby forms a spin configuration that consists of a pair of Néel skyrmion and antiskyrmion. Subsequently, the antiskyrmion breaks as a result of its energetic instability, as shown in Fig. 16(c). In addition, both experiments and simulations indicate the skyrmion creation efficiency is optimum when the length scale of the effective torque matches the size of the skyrmion. In Ref. 61 the size of the skyrmion is relatively large, within the range of 2–6 μm, corresponding to the SAW wavelength of 8–32 μm. In order to reduce the computation work, the simulation employs the SAW wavelength around 100 nm and thus predicts the skyrmion size of ∼20 nm. For the convenience of applications, a 10-nm range skyrmion is desirable. Therefore, further experimental efforts are required to fabricate higher-frequency SAW devices. Additionally, the SAWs did not drive the skyrmions, which is probably accounted for by large pinning potentials in the films deposited on LiNbO₃ substrates.⁶¹ Recent experiments^157,262 using optical methods to excite SAWs can help realize SAW-driven skyrmion motion, and especially the experimental capability of focusing the SAW down to ∼100 nm⁵⁶ may even enable acoustic manipulation of a single skyrmion motion.

In this article, we have reviewed advances in the acoustic control of magnetism in the past decade. Overall, acoustic manipulation is a promising strategy because of its fast and energy-efficient nature, which is particularly desirable for technological applications. Herein, we have endeavored to present a variety of popular magnetic topics associated with the acoustic control, including FMR, magnetic damping, spin pumping, skyrmions, magnonic crystals, domain wall motion, precessional switching, nonlinear spin dynamics, AOS, STT switching, and THz radiation. It is worth noting that many of them are still emerging research fields with great potential of applications. For instance, the creation of skyrmions by an acoustic wave was recently demonstrated,⁶¹ but acoustic control of skyrmion motion and nanoscale skyrmion creation remains challenging. SAW-assisted STT switching needs to be experimentally implemented, although the simulations^140,141 have predicted the viability of SAW-facilitated STT switching. Numerical simulations²⁶³ have predicted a strain-mediated spin–orbit torque (SOT) switching. Instead of applying an external field, the strain-induced MEL anisotropy can be used to break lateral symmetry and thereby enable a field-free deterministic out-of-plane switching. Therefore, SAW-mediated SOT switching can be envisioned. In addition, the acoustic control of magnetism could be expanded even further. Magnetoelastic phenomena in an antiferromagnet,^264,265 have been observed, and thus, one may expect the acoustic resonant excitation of an antiferromagnet at THz frequencies and thereby THz spin pumping^266,267 using THz acoustic waves,²⁶⁸ as a lattice vibration-driven spin system in a THz regime was observed in a ferromagnet.²⁶⁹ Beyond “magnetism,” acoustic waves recently have been applied to manipulate spin states in semiconductor silicon carbide via spin-acoustic resonance.²⁷⁰ The absorption of the SAWs in graphene^271,272 and topological insulators²⁷³ have been theoretically investigated, which may suggest the possibility of the acoustic control of graphene and topological insulator spintronics,^274,275 which may open brand new intriguing research fields. The field of acoustic manipulation of magnetism is poised to make further significant breakthroughs, and we hope that the review stimulates further research activities of the fascinating coupled physical phenomena between spin and lattice degrees of freedom and their potential applications.

This work was supported by the National Science Foundation under Grant Nos. ECCS-1509020 and DMR-1506104. We acknowledge Wei Han for his helpful suggestions for the manuscript.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.