Surface Spin Waves in the Heisenberg Antiferromagnet with Changes in Exchange and Anisotropy Constants at the 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.