Spin Pumping and Enhanced Gilbert Damping in Thin Magnetic Insulator Films

Precessing magnetization in a thin-film magnetic insulator pumps spins into adjacent metals; however, this phenomenon is not quantitatively understood. We present a theory for the dependence of spin pumping on the transverse mode number and in-plane wave vector. For long-wavelength spin waves, the enhanced Gilbert damping for the transverse mode volume waves is twice that of the macrospin mode, and for surface modes, the enhancement can be ten or more times stronger. Spin pumping is negligible for short-wavelength exchange spin waves. We corroborate our analytical theory with numerical calculations in agreement with recent experimental results.