Spin Diffusion and Propagating Modes in Anisotropic Paramagnet

Abstract

Approximate nonlinear, integral equations for the spectral functions of the longitudinal and the transverse correlations are derived. From these, the rate at which local fluctuations in magnetization density diffuse is calculated for nearest‐neighbor interactions in an anisotropic paramagnet, $$\mathcal{H}\mathrm{=-}{\displaystyle \sum _{\mathrm{i,j}}}{I}_0{\mathrm{(ij)[S}}_i^z{S}_j^z{\mathrm{+\gamma (S}}_i^x{S}_j^x{\mathrm{+S}}_i^y{S}_j^y\mathrm{)]}$$ , with sc and bcc structures. At high temperatures, the diffusion constant is found to be $$D_0\mathrm{=(}\frac{1}{3}{\mathrm{)\gamma }}^2{\mathrm{zI}}_0{a}^2{\text{[πs(s+1)/3z(1+γ}}^2{\mathrm{)]}}^{\text{1/2}}$$ , where a is the nearest‐neighbor distance and z is the coordination number. For the isotropic case, i.e., γ=1, the structure of the spectral function is examined for the existence of propagating modes. It is concluded that at high temperatures i.e., βJ(0)≪1, no observable propagating modes with adequate thermodynamic weight exist. It turns out, however, that near T_c for Ka>[χ(0, 0)]^−1/2, propagating modes, E_K, with adequate thermodynamic weight are possible. One finds E_K∼(Ka)^5/2 and D₀K²∼χ^−1/4(0, 0) (Ka)².