Spin waves in dilute ferromagnets: Cluster-Bethe-lattice approach

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Abstract
A calculation of the local density of spin-wave states in a dilute ferromagnet is presented. It is based on a Green's-function formulation solved within the cluster-Bethe-lattice approximation. The method is compared with an exact solution for the one-dimensional dilute ferromagnet. We also study clusters of nine atoms in the bcc structure, and clusters of 7, 19, and 27 atoms in the simple-cubic structure. Our study shows: (i) a stability condition for ferromagnetism in agreement with percolation theory; (ii) a local structure dependence of the spin-wave structure; (iii) the existence of localized spin-wave states due to both isolated magnetic clusters and nonpropagating magnon modes.