Critical and Spin-Wave Fluctuations in Nickel by Neutron Scattering

This paper gives direct measurements of the frequency- and wave-vector-dependent critical scattering of neutrons from nickel. Extensive measurements have been made around the Curie temperature to study the critical fluctuations in detail, particular emphasis being placed on the dynamics of these fluctuations. Below the Curie temperature Tc, the fluctuations can be described in terms of spin-wave excitations with an exchange stiffness constant D that varies with temperature as (1-TTc) to the power 0.39±0.04. The spin waves become over-critically damped just below Tc. Right at the critical temperature, the energy width of the scattering is observed to vary as the wave vector q to the power 2.46±0.25, in excellent agreement with the predictions of the dynamic scaling laws. Above Tc, in the hydrodynamic region, the spin-diffusion constant is observed to vary as (1-TcT) to the power 0.51±0.05, in marked contrast to theoretical predictions of a value close to 0.33. Comparison with our recent data for iron suggests that spin diffusion in the two materials may be occurring with different dominant mechanisms. As in iron, no scattering was observed from diffusive components of the susceptibility for T