Contribution to the Spin-Wave Theory of a Dilute Heisenberg Ferromagnet

A spin-wave theory of a dilute Heisenberg ferromagnet is studied using Green's function techniques. The Green's function for one-magnon excitations is calculated in two ways, a decoupling method and a diagram method. An expression for energy is applied to determine the critical concentration for which the ferromagnetic ground state is unstable with respect to the formation of long-wavelength spin waves. For a simple cubic crystal, the result lies close to that obtained using a cluster expansion method. §I. Introduct:i.on The spm-wave theory of a ferromagnetic crystal, contammg some concen tration of magnetic atoms of another sort, has been studied by several authors. 1 ) The problem is similar to the lattice vibration problem in which both the mass and the effective atomic force constants are changed. The structure of the energy spectrum which has been obtained within the framework of one-vertex approxi mation reflects the existence of localized or quasi-localized levels in the single impurity problem.