Coupled magnetic and elastic dynamics generated by a shear wave propagating in ferromagnetic heterostructure

摘要

Using advanced micromagnetic simulations, we describe the coupled elastic and magnetic dynamics induced in ferromagnetormal metal bilayers by shear waves generated by the attached piezoelectric transducer. Our approach is based on the numerical solution of a system of differential equations, which comprises the Landau-Lifshitz-Gilbert equation and the elastodynamic equation of motion, both allowing for the magnetoelastic coupling between spins and lattice strains. The simulations have been performed for heterostructures involving a Fe_(81)Ga_(19) layer with the thickness ranging from 100 to 892 nm and a few-micrometer-thick film of a normal metal (Au). We find that the traveling shear wave induces inhomogeneous magnetic dynamics in the ferromagnetic layer, which generally has an intermediate character between coherent magnetization precession and the pure spin wave. Owing to the magnetoelastic feedback, the magnetization precession generates two additional elastic waves (shear and longitudinal), which propagate into the normal metal. Despite such complex elastic dynamics and reflections of elastic waves at the Fe_(81)Ga_(19)|Au interface, periodic magnetization precession with the excitation frequency settles in the steady-state regime. The results obtained for the magnetization dynamics at the Fe_(81)Ga_(19)|Au interface are used to evaluate the spin current pumped into the Au layer and the accompanying charge current caused by the inverse spin Hall effect. The calculations show that the dc component of the charge current is high enough to be detected experimentally even at small strains ~10~(-4) generated by the piezoelectric transducer.