Magnetic Surface Modes Obtained by a Simple Method

A simple method of obtaining the normal modes of ferromagnetic and antiferromagnetic systems is presented and used to classify surface modes. Since all spins precess at the same frequency in a normal mode, the frequency and spin configurations can be obtained from the equations of motion of one or sometimes two spins near the surface. The method affords a clear physical understanding of the surface modes and requires very little calculation. One class of surface modes is the changed-parameter class, in which the missing neighbors of a surface spin are compensated for by a changed parameter such as an exchange constant at the surface. Another is the equivalent-layer class, in which the crystal consists of equivalent layers such that the net torque on each spin S1 on the surface of each layer exerted by all spins on the surface side of S1 is zero.