Macroscopic and Microscopic Theories of Dipole-Exchange Spin Waves in Thin Films: Case of the Missing Surface States

Abstract

Calculations of dipole-exchange spin waves in thin films using a microscopic model show no evidence of surface modes above the lowest bulk frequency, in contrast to recent results based on a macroscopic model. The apparent absence of the surface branch in the former model is explained in terms of the admixture of bulk and surface waves. Nearly exact quantitative agreement between the two models is obtained for wave vectors as large as ${10}^7$ ${\mathrm{cm}}^{-1\mathrm{}}$.