  We develop a self-consistent theory for current-induced spin wave excitations
in normal metal-magnetic insulator bilayer systems, thereby establishing the
relation between spin wave excitation and the experimentally controlled
parameters. We fully take into account the complex spin wave spectrum including
dipolar interactions and surface anisotropy as well as the spin-pumping at the
interface. Our results focus on the mode-dependent power close to the critical
currents for spin wave excitation. The major findings are (a) the spin transfer
torque can excite different spin-wave modes simultaneously; (b) spin pumping
counterbalances spin-transfer torque and affects the surface modes more than
the bulk modes; (c) spin pumping inhibits high frequency spin-wave modes,
thereby redshifting the excitation spectrum. We can get agreement with
experiments on yttrium iron garnet|platinum bilayers by postulating the
existence of surface anisotropy modes.
