Surface Spin Waves for the Simple Cubic Antiferromagnet

The surface spin-wave spectra of a simple cubic two-sublattice antiferromagnet is derived for a {100} surface as a function of the ratio $\epsilon$ of the surface exchange to the bulk exchange. The effects of changes in the surface anisotropy are also included. In general, a doubly-degenerate acoustical- or optical-type surface branch is found, depending upon the value of $\epsilon$. For $-0.112<\epsilon <1.107\mathrm{}$, an acoustic branch exists over the entire two-dimensional Brillouin zone. If $1.107<\mathrm{}\epsilon <1.207\mathrm{}$, then the branch is truncated at small values of the propagation vector $k$ parallel to the surface. In the range $1.207<\mathrm{}\epsilon <1.25\mathrm{}$, no surface states exist for the nearest-neighbor-exchange model. When $1.25<\mathrm{}\epsilon <1.854\mathrm{}$, a truncated optical-type branch exists. A complete optical branch exists for $\epsilon \ge 1.854$. The $k=0\mathrm{}$ surface-antiferromagnetic-resonance (SAFMR) mode lies very near the bulk AFMR mode for a wide range of surface perturbation parameters. The SAFMR mode is found to be of very long range when the anisotropy energy is small compared to the exchange energy. For simple cubic RbMn${\mathrm{F}}_3$, the SAFMR mode is estimated to have a range on the order of 200 μ.