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.
We present a simple conceptual discussion of the competition between hybridization and exchange in the problem of magnetic-nonmagnetic transitions in intermediate-valence systems.Two atomic-like calculations are presented: a singlet-doublet and a doublet-doublet level systems. A phenornenological ferromagnetic coupling is introduced. In the singlet-doublet case, three distinct phases are possible: paramagnetic, induced ferromagnetic, and ferromagnetic, depending on the values of the parameters. Results for the enhanced susceptibility are also presented, In the doublet-doublet case, two phases occur, paraand ferromagnetic. The valence change upon ordering is discussed. We argue that not only the "magnetic" character of the configuration, but also the relative strength of the local-moment quenching component of the hybridization potential and of the exchange interaction, are important in determining the existence of a spontaneously polarized phase.
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