Temperature Dependence of Spin-Wave Energy in thet-Matrix Approximation

A Green's-function method is used to determine the spin-wave energy at finite temperatures in the itinerant model for a ferromagnet. The formalism, which was developed in a previous paper, is based on the $t$-matrix approximation in a one-band model, using the Hubbard Hamiltonian. Within this approximation, a formal expression is obtained for the spin-wave dispersion relation valid for all values of the wave vector $\overrightarrow{\mathrm{q}}$ in the low-density limit. From this, the spin-wave energy at low temperatures, expressed in the form $C_0=C_T{T}^2$, is evaluated for a fcc lattice with first- and second-neighbor interactions. The value obtained for $C_T$, using a reasonable set of band parameters, is consistent with that obtained experimentally.