Critical scattering in magnetite

Abstract

The energy and wave-vector dependence of the magnetic critical scattering in magnetite has been measured in the vicinity of the 111, 220, and 222 reciprocal-lattice points using a triple-axis neutron spectrometer. The spectral shape function has been found to be Gaussian at the critical point with a characteristic frequency proportional to ${q}^{z}$, where $Z=2.28\ifmmode\pm\else\textpm\fi{}0.05,2.30\ifmmode\pm\else\textpm\fi{}0.10, \mathrm{and} 2.35\ifmmode\pm\else\textpm\fi{}0.10$, for wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ measured from 111, 220, and 222, respectively. These values are in reasonable agreement with the dynamic scaling prediction of 2.5. At ${T}_{c}$, the wave-vector-dependent susceptibilities in the vicinity of the three magnetic reflections agree with calculations of de Gennes and Villain. In the spin-wave region, the stiffness constant was found to renormalize with critical index ${\ensuremath{\sigma}}^{\ensuremath{'}}=0.32\ifmmode\pm\else\textpm\fi{}0.013$, which compares favorably with the value 0.33 predicted by dynamic scaling. Above ${T}_{c}$ the inverse range parameter, as determined from three-crystal measurements, showed no site dependence; the critical index $\ensuremath{\nu}$ was found to be 0.79 \ifmmode\pm\else\textpm\fi{} 0.02. Characteristic frequencies of the spectral shape function, measured above ${T}_{c}$, are discussed in relation to the predictions of R\'esibois and co-workers.