Critical scattering in magnetite

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 $Z=2.28\mathrm{}\pm 0.05,2.30\pm 0.10, \mathrm{and} 2.35\pm 0.10$, for wave vector $\overrightarrow{\mathrm{q}}$ 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 ${\sigma }^{\prime }=0.32\mathrm{}\pm 0.013$, 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 $\nu$ was found to be 0.79 ± 0.02. Characteristic frequencies of the spectral shape function, measured above $T_c$, are discussed in relation to the predictions of Résibois and co-workers.