Temperature variation of surface-spin-wave frequencies in the Heisenberg ferromagnet: The exchange-dominated regime

Abstract

We develop the theory of the temperature variation of surface-spin-wave frequencies in the semi-infinite Heisenberg ferromagnet, for modes with wavelength sufficiently short that exchange interactions provide the dominant contribution to the excitation energy. Magnon-magnon interactions are the source of the temperature variation of the surface-spin-wave energies, and our attention is directed toward the leading contribution in the limit of low temperatures. We find a $T^{\frac{5}{2}}$ correction to the $T=0\mathrm{}$ spin-wave frequencies, so the leading term exhibits the same temperature variation as found for bulk spin waves.