Spin dynamics of Gd at high temperatures

The magnetic excitation spectra of Gd were measured by neutron inelastic scattering over the entire Brillouin zone in the 〈110〉 direction at temperatures from 250 to 850 K ($T_c$=293 K). The data were fitted to a damped-harmonic-oscillator form for the spectral weight function and were placed on an absolute cross-section basis. Wave-vector-dependent susceptibilities were obtained by integration over energy. They clearly show the presence of static spin correlations even at T=850 K. At T≥$T_c$ we observe a crossover from spin-diffusive motion at small q to spin-wave behavior at large q. The wave vector $q_c$ at which this crossover occurs is determined by the ratio of the damping parameter to the second moment, 〈${\omega }^2$〉, of the frequency distribution. Surprisingly, 〈${\omega }^2$〉 remains independent of temperature above $T_c$, and the temperature dependence of $q_c$ is therefore determined by a gradual change in the damping. This results in a very weak $q_c$-versus-T dependence, which is not consistent with a magnetic short-range-order interpretation for the existence of spin waves above $T_c$.