PHENOMENOLOGICAL MOLECULAR FIELD THEORY OF THE MOTT-WIGNER TRANSITION IN MAGNETITE

摘要

The measurement by Verwey and Haayman of the variation of the transition temperature of magnetite with stoichiometry is discussed in terms of the molecular field solution of a lattice gas model of the Mott-Wigner insulator to metal transition. This model gives rise to a second order phase transition. The observed first order transition is reproduced by substituting a phenomenologically screened interaction, in which the dielectric constant causing the screening decreases with increasing order parameter. Since the phenomenological screening necessary to produce the observed results is very large compared to that expected on the basis of electronic screening, we postulate that the dielectric constant includes the effect of local charge polarization accompanying the ordering. It is possible to obtain a consistent picture of much of the experimental data on magnetite using this model. Inelastic neutron scattering and optical absorption are discussed as means of observing the elementary excitations of the system and to deduce some of the parameters in the theory. The low-lying excitations in the ordered (i.e., insulating) state are shown to be excitons with flat dispersion (i.e., their energies do not depend on wave-vector); their energies and cross sections are calculated.