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

Abstract

The dependence of the surface spin-wave eigenmodes on the ratio of the surface exchange to the bulk exchange ${\epsilon }_{\perp }$, and on the surface anisotropy energy for {100} surfaces of a bcc antiferromagnet is calculated. For $0<~{\epsilon }_{\perp }<~1$, 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 $1<\mathrm{}{\epsilon }_{\perp }<2\mathrm{}$, we also find two surface-wave branches: a complete $+E$ acoustic branch which approaches the bulk curve as ${\epsilon }_{\perp }\to 2$, and also a $-E$ optical-type branch which is cut off at small k. Finally, for ${\epsilon }_{\perp }>2\mathrm{}$, 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.