Surface spin waves and surface spin correlations in the presence of magnetic surface reconstruction

We examine the nature of surface spin waves in a ferromagnetic crystal for which the surface spin configuration is unstable with respect to ferromagnetic alignment. Magnetic surface reconstruction then occurs, and the spectrum of surface spin waves is found to differ qualitatively from the case where the spins align ferromagnetically. In particular, with the reconstructed phase, there is a surface-spin-wave branch with a dispersion relation Ωₛ(k_∥) that approaches zero linearly with k_∥, as k_∥ vanishes. In the long-wavelength limit, the spin deviation associated with the mode is localized to the surface. While we consider only a simple model here, we argue that symmetry considerations lead to the existence of such modes whenever magnetic surface reconstruction occurs. We also examine the nature of spin fluctuations in the reconstructed state by studying the behavior of spin correlation functions for a two-dimensional layer of canted spins in a strong exchange field. Large-amplitude spin fluctuations occur in the presence of the low-frequency surface wave; these fluctuations are subdued by the presence of surface anisotropy fields.