THE EFFECT OF SURFACES ON THE PROPERTIES OF MAGNETIC MATERIALS

Abstract

In the first portion of the paper, we derive the form of the T-matrix that describes the scattering of a magnon from the surface of a Heisenberg ferromagnet. The model employed allows the exchange constants in the surface layer of spins to differ from the values appropriate to the bulk crystal. We also obtain the form of the T-matrix without the need to specify the detailed geometrical arrangement of spins in the layers parallel to the surface, or the range of the exchange interaction in directions parallel to the surface. The T-matrix, and the resulting Green's function may thus be applied to compute properties of the semi-infinite crystal for a wide variety of geometries. In this work, we obtain the surface magnon dispersion relation by examining the poles of the T-matrix. The results are illustrated with applications to a specific model considered by Fillipov, where acoustical surface magnons below the bulk spin wave band, or optical surface magnons above the bulk band may result. We then use the T-matrix to compute the lifetime of spin waves from scattering off the surface. We find the lifetime τ(k) of a spin wave of wave vector k is given by the simple expression τ = L/|[MATH].VG(k)| where L is the crystal thickness, [MATH] a unit vector normal to the surface, and VG(k) the magnon group velocity. This result is valid even for large values of k, and is unaffected by changes in exchange constants near the surface. In a second portion of the paper, we provide a brief review of recent theoretical studies of the semi-infinite Heisenberg ferromagnet. The behavior of the mean spin deviation near the surface, and the effect of surface pinning fields and changes in the exchange constants near the surface on the surface specific heat will be examined. Some features of the theory of low energy electron scattering from the magnetic degrees of freedom will be described. Finally, the properties of surface magnons in antiferromagnets and the surface spin flop transition will be discussed briefly.