Longitudinal spin fluctuations in nickel

Abstract

The longitudinal, transverse, and paramagnetic spin fluctuations in Ni have been measured near ${\mathit{T}}_{\mathit{C}}$ by means of polarized neutron scattering in the momentum range 0.06q0.18 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$. In transverse scans, spin-wave peaks at ${\mathrm{\ensuremath{\omega}}}_{\mathit{q}}$=${\mathit{Dq}}^{2}$ appear as expected from previous measurements performed with unpolarized neutrons. The longitudinal fluctuations are quasielastic, in agreement with predictions of a recent mode-mode coupling theory and renormalization-group theory. The data indicate that the longitudinal dynamical scaling function is smaller than 1 just below ${\mathit{T}}_{\mathit{C}}$. The scaling function for the paramagnetic scattering is shown to be in agreement with the R\'esibois-Piette scaling function for energy scales up to ${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{C}}$. The measured field dependence of the scattering is rather weak, indicating that the internal fields H are rather large. Therefore it was impossible to observe the ${\mathit{H}}^{\mathrm{\ensuremath{-}}1/2}$ divergence of ${\mathrm{\ensuremath{\chi}}}_{\mathit{L}}$(q\ensuremath{\rightarrow}0) that is predicted for the isotropic Heisenberg model in three dimensions. In contrast, we found ${\mathrm{\ensuremath{\chi}}}_{\mathit{L}}$(q\ensuremath{\rightarrow}0)\ensuremath{\propto}(1-T/${\mathit{T}}_{\mathit{C}}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$, which also appears to be a result of the internal fields. The q dependence of ${\mathrm{\ensuremath{\chi}}}_{\mathit{L}}$ is Lorentzian-like. The T dependence of the correlation length indicates critical behavior. These features closely resemble the behavior of the paramagnetic fluctuations, and they are in agreement with results obtained with use of \ensuremath{\epsilon}-expansion techniques.