Calculation of spin-wave modes for a stepped surface in a Heisenberg ferromagnet

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Abstract
We present a transfer-matrix calculation of the spin-wave spectrum of a face-centered-cubic ferromagnet with a stepped-surface structure. The calculation is based on a Heisenberg Hamiltonian with nearest-neighbor interaction only. It does not include either anisotropy terms or relaxation and reconstruction at the surface. It is found that localized step modes exist in the vicinity of the step edge and that atoms in that neighborhood are magnetically softer than ordinary surface atoms. Spin-wave spectra and magnetization versus temperature curves are presented for atoms at various positions.