  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.
