Temperature-dependent light-scattering studies of the Verwey transition and electronic disorder in magnetite

Abstract

The light-scattering spectra of magnetite (${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$) have been studied as a function of temperature in an attempt to determine the role played by optical phonons in the Verwey transition. A group-theoretical analysis of the long-wavelength phonons is used to classify the normal modes in both the cubic and orthorhombic phases. In addition, a molecular model of magnetite is described and is used as a basis for the derivation of the symmetry coordinates of all 42 normal modes in the cubic structure. Experimentally, five Raman modes are observed in the cubic phase ($T>\mathrm{}119\mathrm{}$ K) in agreement with the predictions of group theory; likewise, five modes are observed in the orthorhombic phase ($T<\mathrm{}119\mathrm{}$ K) even though 15 Raman-active modes are expected in this phase. On passing through the transition temperature, no abrupt or dramatic changes are observed either in the general features of the light-scattering spectrum or in the phonons themselves. We interpret this lack of a sudden change as evidence that the Raman-active phonons play a minor role in the physical mechanism responsible for the transition. Furthermore, these results appear to be inconsistent with the predictions of both the Verwey model and various band models that have been recently proposed. A particularly unusual feature of the Raman spectrum is that the Raman lines are anomalously broad ($\approx 30$ ${\mathrm{cm}}^{-1\mathrm{}}$) even at low temperatures. For the highest-frequency mode ($\approx 680$ ${\mathrm{cm}}^{-1\mathrm{}}$), the linewidth increases continuously as the temperature is raised through and above the transition temperature. We interpret the broadening at low temperatures as being due to electronic disorder associated with the random arrangement of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions on the $B$ sites. This is in distinct contrast to the basic assumptions of the Verwey model. On the other hand, it is suggested that the temperature-dependent part of the linewidth is related to the conduction mechanism in magnetite, which we assume to be due to small-polaron hopping. Arguments are presented in support of this assumption.