Temperature dependence of the dynamic susceptibility of nickel

Abstract

The coherent magnetic inelastic scattering of neutrons has been used to measure the dynamic susceptibility $\chi (\overrightarrow{\mathrm{q}},\omega )$ of nickel from low temperatures to well above the ferromagnetic transition temperature. As the temperature approaches $T_C$ from below, the linewidths of the spin waves are found to broaden, and in the small wave-vector region the scattering is in general agreement with dynamic scaling theory. At larger wȧve vectors, however, we find that the observed scattering can be more naturally described in terms of spin-wave-like excitations whose widths $\Delta E$ remain less than the excitation energies $E(\frac{\Delta E}{E}<1)$ for $T>\mathrm{}{T}_C$. The "dispersion relation" for these spin waves is only moderately renormalized up to $T_C$ and then remains constant as the temperature is raised further up to at least twice $T_C$, while the widths continue to broaden slowly above $T_C$. The overall magnitude of the susceptibility decreases with increasing temperatures, but the abrupt decrease of $\chi (\overrightarrow{\mathrm{q}},\omega )$ at high energies, interpreted as the intersection of the collective excitation spectrum with the Stoner continuum of single-particle excitations, is found to be insensitive to the temperature. These results are compared and contrasted with the recent results for iron.