Theory of the dipole-exchange spin wave spectrum in ferromagnetic films with in-plane magnetization revisited
J. Harms, R. A. Duine
Abstract
We present a refinement of the widely accepted spin-wave spectrum that Kalinikos and Slavin (Kalinikos, 1981; Kalinikos and Slavin, 1986) computed for magnetic films with an in-plane magnetization. The spin wave spectrum that follows from the diagonal approximation in this theory becomes inaccurate for relatively thick films, as has already been noted by Kreisel et al. (2009). Rather than solving an integrodifferential equation which follows from the magnetostatic Green’s function, as done by Kalinikos and Slavin (Kalinikos, 1981; Kalinikos and Slavin, 1986), we impose the exchange and magnetostatic boundary conditions on bulk spin-wave solutions. This boundary problem has an accurate analytical solution which is quantitatively different from the commonly used diagonal theory (Kalinikos, 1981; Kalinikos and Slavin, 1986) for magnetic films.