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 ta
ke 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.
