Acoustically Excited Magnetic Dynamics and Spin Flow in Spin-Valve Structures

Abstract

Acoustic waves and strain pulses created by a piezoelectric or optical transducer represent an attractive tool for the generation of spin dynamics in magnetoelastic materials and heterostructures. The advantage of acoustic excitation consists in much lower power consumption compared with the classical excitation by a microwave magnetic field. The magnetization precession driven by elastic waves can be further used for spin pumping into normal metals and semiconductors. Here we describe theoretically the magnetization dynamics and spin flow induced by plane acoustic waves traversing trilayer structures involving two ferromagnetic ($F$) films separated by a layer of normal metal ($N$). The problem is solved by advanced micromagnetoelastic simulations, which allow for the two-way coupling between spins and strains in the $F$ films and their long-range dynamic interaction resulting from the spin flow across the $N$ spacer. To derive the expression for such an interaction, we solve the spin-diffusion equation in $N$ with the account of spin pumping created by dynamically strained $F$ films and spin backflow through the interfaces. Performing numerical simulations for the ${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}{/\mathrm{Au}/\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$ trilayers excited by longitudinal and transverse elastic waves, we quantify the inhomogeneous magnetization precession in the galfenol films and determine the spatial distributions of the oscillating spin current and spin accumulation in the Au spacers of different thickness. These distributions are further used to calculate the mean spin current and total spin accumulation in the spacer. It is found that both ac and dc parts of these quantities exhibit strong variations with the spacer thickness. Remarkably, the nonzero components of the total spin accumulation and mean spin current mostly have pronounced maxima at $\mathrm{Au}$ thicknesses amounting to about 0.25 and 0.75 of the wavelength ${\ensuremath{\lambda}}_{N}$ of the elastic wave in $\mathrm{Au}$, which is explained by an analytical model of strain distribution in the trilayer. Our theoretical results, which shed light on the acoustically excited generation of spin imbalance in magnetoelastic spin-valve structures, could be useful for the development of energy-efficient spin injectors into normal conductors with weak spin-flip scattering.