General Exchange Boundary Condition and Surface Anisotropy Energy of a Ferromagnet

Abstract

The general exchange boundary condition applicable to a line of spins placed in a static field of arbitrary orientation and whose end spins are subjected to different environments are first formulated. The result is then applied to the problem of spin wave resonance in thin magnetic films. Both the line and absorption spectra are calculated assuming different types of surface anisotropy. By comparing our theoretical results with various experiments, it is concluded that the shape of the energy surface of the surface anisotropy energy are uniaxial with the easy axis of magnetization in the direction of the surface normal and the hard plane of magnetization parallel to the film plane. The possible origin of this anisotropy, including the question of dynamic pinning, is discussed in some detail. Aside from the usual volume spin-wave resonance modes, we found also some surface spin wave modes whose presence may have an important bearing upon the magnetization reversal process in thin Permalloy films. An apparent departure from the $k^2$ dispersion low for spin waves and its relevance upon the determination of the exchange constant is also discussed.