Surface Effects in the Heisenberg Antiferromagnet

We have investigated the effect of a free (100) surface on low-temperature properties of a Heisenberg antiferromagnet of the CsCl structure. It is found that a surface magnon branch occurs in the excitation spectrum, with an excitation energy less than the frequency of a bulk magnon of the same wavelength. In the limit of infinite wavelength, the surface magnon frequency for this geometry is ${(H_E{H}_A+{H_A}^2)}^{\frac{1}{2}}$, compared to ${(2\mathrm{}{H}_E{H}_A+{H_A}^2)}^{\frac{1}{2}}$ for bulk magnons of infinite wavelength. In the limit $H_E\gg H_A$, the surface magnon frequency is found to be insensitive to changes in exchange constants or anisotropy fields near the surface. The surface modes may be observed in the infrared absorption spectrum of the material, and will affect the low-temperature thermodynamic properties of the system. By means of a Green's-function method, we have examined the influence of the surface on the infrared absorption spectrum, the specific heat, and the low-temperature form of the parallel susceptibility and mean sublattice deviation. Numerical estimates indicate that the surface corrections of the thermodynamic quantities may be observable when $k_{B}T\ll {\left(2\mathrm{}{H}_E{H}_A\right)}^{\frac{1}{2}}$.