Excitations in the dilute Heisenberg ferromagnet using the coherent potential approximation

The coherent potential approximation (CPA) has been generalized to describe spin waves in a dilute Heisenberg ferromagnet at T=0. The full T matrix of an isolated vacancy in an effective medium is evaluated and the self-energy is obtained selfconsistently. In order to project out the spurious degrees of freedom associated with the fictitious spins on the vacancy sites, a class of pseudopotentials are constructed. The response functions G(k, omega ) and density of states rho ( omega ) for two such pseudopotentials are evaluated in detail. The had core pseudopotential is found to yield the best CPA approximation although it fails near the critical percolation concentration of magnetic sites, as do all the effective medium theories in the face of large fluctuations. The spin-wave stiffness D is calculated and the magnetization and specific heat near T=0. The random phase approximation is used to find T c , the transition temperature.