Nonreciprocal Surface Acoustic Waves in Multilayers with Magnetoelastic and Interfacial Dzyaloshinskii-Moriya Interactions

Abstract

Surface acoustic waves (SAW) propagating in a piezoelectric substrate covered with a thin ferromagnetic/heavy metal bilayer are found to exhibit a substantial degree of nonreciprocity, i.e. the frequencies of these waves are non-degenerate with respect to the inversion of the SAW propagation direction. The simultaneous action of the magneto-elastic interaction in the ferromagnetic layer and the interfacial Dzyaloshinskii-Moriya interaction (IDMI) in the ferromagnetic/heavy metal interface, results in the openings of magneto-elastic bandgaps in the SAW spectrum, and the frequency position of these bandgaps are different for opposite SAW propagation directions. The bandgap widths and the frequency separation between them can be controlled by a proper selection of the magnetization angle and the thickness of the ferromagnetic layer. Using numerical simulations we demonstrate that the isolation between SAWs propagating in the opposite directions in such a system can exceed the direct SAW propagation losses by more than one order of magnitude.

Unidirectional Pumping of Phonons by Magnetization Dynamics

“…We focus on the unidirectional [31] excitation of SAWs via magnetic nanostructures on top of a dielectric substrate that are brought into FMR by external microwaves. We predict effects that are very different from the reported nonreciprocity, i.e., a sound velocity that depends on direction [11,32], which is enhanced in magnetic multilayers on top of a piezoelectric substrate [33][34][35]. The magnetic order of, e.g., a wire on top of a dielectric, does not couple nonreciprocally to the surface phonons in the configuration in Fig.…”

Damping of Magnetoelastic Waves

“…Thus, formulas (12), (13), and (14) allow us to obtain a complete expression for the dissipative function. On its basis, the frequencies of the coupled magnetoelastic oscillations making allowance for the oscillation damping can be calculated.…”

“…Let us consider the oscillations, whose wave vector k is directed along the magnetic moment of the crystal, k ‖ 0 ‖ . In this case, only the following components of the elastic-strain tensor and the gradients of the effective magnetic field remain different from zero: By applying relations (22) to components (12), (13), and (14) of the dissipative function and taking advantage of definitions (21), the following components are obtained: for the magnetic relaxation term, For further calculations, let us expand the total energy density (2) in a power series in small deviations m(r, ) and…”

“…This is a consequence of numerous experimental studies [8][9][10][11] carried out with magnetically ordered systems, where the magnetoelastic interaction can be rather strong [10,11]. The results of modern researches, both experimental [11] and theoretical [12], testify to the creation of special conditions for the propagation of oscillations under the influence of the magnetoelastic interaction. The latter can lead to the non-consistent propagation of both the spin and elastic waves in multilayer structures of various types [11,12].…”

“…The results of modern researches, both experimental [11] and theoretical [12], testify to the creation of special conditions for the propagation of oscillations under the influence of the magnetoelastic interaction. The latter can lead to the non-consistent propagation of both the spin and elastic waves in multilayer structures of various types [11,12]. The corresponding results may testify that the influence of the magnetoelastic interaction can be used in modern functional elements applied for the quantum information processing and based on the magnonics and magnetic spintronics principles [13,14].…”