Spin Pumping, Dissipation, and Direct and Alternating Inverse Spin Hall Effects in Magnetic Insulator-Normal Metal Bilayers

TL;DR

This paper provides a theoretical analysis of how spin pumping enhances Gilbert damping and generates inverse spin Hall voltages in magnetic insulator-normal metal bilayers, revealing mode-dependent effects and the influence of surface anisotropy.

Contribution

It introduces a comprehensive theoretical model linking spin-wave modes, damping enhancement, and inverse spin Hall voltages, including effects of surface anisotropy and mode localization.

Findings

Damping enhancement ratio of 2 in the long-wavelength limit for transverse volume modes.

Surface anisotropy can increase damping enhancement by an order of magnitude.

Inverse spin Hall voltages are proportional to magnetic energy and are mode-dependent.

Abstract

We theoretically consider the spin-wave mode- and wavelength-dependent enhancement of the Gilbert damping in magnetic insulator--normal metal bilayers due to spin pumping as well as the enhancement's relation to direct and alternating inverse spin Hall voltages in the normal metal. In the long-wavelength limit, including long-range dipole interactions, the ratio of the enhancement for transverse volume modes to that of the macrospin mode is equal to two. With an out-of-plane magnetization, this ratio decreases with both an increasing surface anisotropic energy and mode number. If the surface anisotropy induces a surface state, the enhancement can be an order of magnitude larger than for to the macrospin. With an in-plane magnetization, the induced dissipation enhancement can be understood by mapping the anisotropy parameter to the out-of-plane case with anisotropy. For shorter wavelengths, we compute the enhancement numerically and find good agreement with the analytical results in the applicable limits. We also compute the induced direct- and alternating-current inverse spin Hall voltages and relate these to the magnetic energy stored in the ferromagnet. Because the magnitude of the direct spin Hall voltage is a measure of spin dissipation, it is directly proportional to the enhancement of Gilbert damping. The alternating spin Hall voltage exhibits a similar in-plane wave-number dependence, and we demonstrate that it is greatest for surface-localized modes.