Temperature Dependence of the Ferromagnetic-Resonance Linewidth

A calculation of the temperature dependence of the magnetic-resonance linewidth in ferromagnetic crystals is presented. It is based on the Kubo-Tomita relaxation function and Van Vleck's method of moments, generalized to finite temperatures. Our work differs from previous general theories in that detailed calculations are performed including the applied field so that meaningful comparison between theory and experiment is possible over a wide range of temperatures including the Curie region. The temperature dependence of the moments is calculated in two steps. First, the four- and six-spin correlation functions which occur in the second and fourth moments, respectively, are decoupled into sums of products of two-spin correlation functions. These two-spin thermal averages are then computed in the constant-coupling approximation, since we show that nearest-neighbor static correlations are by far the most important. In this manner linewidth calculations are made for two ferromagnets, ${\mathrm{K}}_2$Cu${\mathrm{Cl}}_4$ · 2${\mathrm{H}}_2$O and Ni, for temperatures ranging from $T=0\mathrm{}$ K to $T=10\mathrm{}{T}_C$. It is found that the method gives reasonable agreement with the experiments of Ford and Jeffries on ${\mathrm{K}}_2$Cu${\mathrm{Cl}}_4$ ·2${\mathrm{H}}_2$O and of Bhagat and Chicklis and of Salamon on Ni.