Spin waves at the surface of dilute ferromagnets

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Abstract
Spin-wave spectra for the (110) surface of a body-centered-cubic dilute ferromagnet are studied. The calculation is a cluster—Bethe-lattice approximation based on a Heisenberg Hamiltonian with nearest-neighbor interactions only. Results are given in terms of various probability parameters which relate to the existence of two nearest-neighbor magnetic atoms at the surface and in the bulk. Depending on these parameters there may be: (1) bands of surface states at energies either (1a) lower than the bulk states or (1b) higher than the bulk states; (2) localized modes at finite energies and below the band states. Results for the surface local magnetization as a function of temperature are presented.