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We theoretically consider the spin-wave mode- and wavelength-dependentenhancement of the Gilbert damping in magnetic insulator--normal metal bilayersdue to spin pumping as well as the enhancement's relation to direct andalternating inverse spin Hall voltages in the normal metal. In thelong-wavelength limit, including long-range dipole interactions, the ratio ofthe enhancement for transverse volume modes to that of the macrospin mode isequal to two. With an out-of-plane magnetization, this ratio decreases withboth an increasing surface anisotropic energy and mode number. If the surfaceanisotropy induces a surface state, the enhancement can be an order ofmagnitude larger than for to the macrospin. With an in-plane magnetization, theinduced dissipation enhancement can be understood by mapping the anisotropyparameter to the out-of-plane case with anisotropy. For shorter wavelengths, wecompute the enhancement numerically and find good agreement with the analyticalresults in the applicable limits. We also compute the induced direct- andalternating-current inverse spin Hall voltages and relate these to the magneticenergy stored in the ferromagnet. Because the magnitude of the direct spin Hallvoltage is a measure of spin dissipation, it is directly proportional to theenhancement of Gilbert damping. The alternating spin Hall voltage exhibits asimilar in-plane wave-number dependence, and we demonstrate that it is greatestfor surface-localized modes.

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