Dynamical spin phenomena generated by longitudinal elastic waves traversing CoFe2O4 films and heterostructures

Abstract

Electric-field control of spin dynamics in ferromagnetic films and heterostructures is crucial for the development of advanced spintronic devices with ultralow power consumption. Such control can be achieved via the magnetoelastic coupling between spins and strains created in a ferromagnet by the attached piezoelectric transducer. The efficiency of strain-mediated excitation and manipulation of spin phenomena is expected to increase drastically in materials with high magnetoelastic coefficients, such as cobalt ferrite. Here we report the state-of-the-art micromagnetic simulations of the spin dynamics arising in ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ films and ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$/Pt bilayers traversed by longitudinal elastic waves. To fully allow for the magnetoelastic coupling, we numerically solve a system of differential equations involving the Landau-Lifshitz-Gilbert equation for the magnetization and the elastodynamic equation for the mechanical displacement. The simulations show that, despite high Gilbert damping characteristic of cobalt ferrite, the injected elastic waves with frequencies around the resonance frequency of coherent magnetization precession in unstrained ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$ film efficiently generate spin waves in this ferrimagnetic insulator. Furthermore, the generated spin wave, which has the wavelength of the driving acoustic wave, creates two secondary elastic waves due to the magnetoelastic feedback. In addition, it modifies the driving elastic wave, leading to the sound attenuation of magnetic origin with decay length about 70 $\ensuremath{\mu}\mathrm{m}$. In ${\mathrm{CoFe}}_{2}{\mathrm{O}}_{4}$/Pt bilayers, the magnetization precession at the interface gives rise to a spin current flowing in the Pt layer, which creates additional damping of the precession and generates a charge current via the inverse spin Hall effect. Remarkably, a circular charge flow is predicted for thick Pt layers, which leads to inhomogeneous potential distributions along their surfaces. The magnitude of the voltage between lateral sides of the Pt layer may exceed 1 nV, which can be measured experimentally.