Critical and Spin-Wave Fluctuations in Nickel by Neutron Scattering

Abstract

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 ${T}_{c}$, the fluctuations can be described in terms of spin-wave excitations with an exchange stiffness constant $D$ that varies with temperature as ($1\ensuremath{-}\frac{T}{{T}_{c}}$) to the power 0.39\ifmmode\pm\else\textpm\fi{}0.04. The spin waves become over-critically damped just below ${T}_{c}$. 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\ifmmode\pm\else\textpm\fi{}0.25, in excellent agreement with the predictions of the dynamic scaling laws. Above ${T}_{c}$, in the hydrodynamic region, the spin-diffusion constant is observed to vary as ($1\ensuremath{-}\frac{{T}_{c}}{T}$) to the power 0.51\ifmmode\pm\else\textpm\fi{}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 $T<{T}_{c}$, this result contrasts strongly with the scattering observed from the Heisenberg antiferromagnet RbMn${\mathrm{F}}_{3}$, where a diffusive mode is clearly seen. Extensive data have been taken of the spin-wave dispersion relations at room temperature. Interpretation of the data in terms of a Heisenberg model leads to the conclusion that the exchange is long-range in extent, with ferromagnetic interactions present over short ranges and antiferromagnetic interactions predominating over longer ranges.