SURFACE SPIN WAVES IN HEISENBERG ANTIFERROMAGNET WITH CHANGES IN EXCHANGE AND ANISOTROPY CONSTANTS AT SURFACE

The dependence of the surface spin-wave eigenmodes on the ratio of the surface exchange to the bulk exchange ε, and on the surface anisotropy energy for {100} surfaces of a bcc antiferromagnet is calculated. For 0<~ε<~1, we find two acoustic-type surface spin-wave branches associated with left-hand +E and right-hand -E circular polarization, both of which are lower in energy than the corresponding bulk modes. The +E mode exists for all values of the two-dimensional propagation vector parallel to the surface, k, which belong to the first Brillouin zone. The -E acoustic surface-state branch is incomplete, being truncated at small k, and has maximum excitation amplitude on the second layer of spins-in contrast to the above mentioned +E branch, which has its maximum on the surface. The truncation of a surface branch occurs whenever decay into the bulk continuum states is possible. In the range 1<ε<2, we also find two surface-wave branches: a complete +E acoustic branch which approaches the bulk curve as ε→2, and also a -E optical-type branch which is cut off at small k. Finally, for ε>2, there are three surface spin-wave branches: +E acoustic branch which is truncated at large k, and complete +E and -E optical branches. The eigenvectors for these modes are also derived. © 1969 The American Physical Society.