Magnetic mean-field modelling of solid solutions: theoretical foundations and application to the hematite–ilmenite system

Abstract

A spatially averaged mean-field model for fully or partially ordered members of the ilmenite–hematite solid solution series is rigorously derived from the Heisenberg Hamiltonian by first assuming no temporal correlation of atomic spins, and then by spatially averaging over spins at equivalent atomic positions. The model is based on the geometry of exchange interactions between nearest and next-nearest neighbours and predicts magnetization curves in homogenous solid solutions with variable degree of order. While the general framework presented can also be applied to atomic scale models, and to other solid solution series, here the symmetries of the ilmenite–hematite lattice are exploited to show that four different sublattice magnetizations and six independent combinations of exchange constants determine the temperature variation of the magnetization curves. Comparing measured Curie temperatures TC and Ms(T) curves to model predictions results in accurate constraints for these combinations. It is also possible to calculate predictions for high-field magnetization slopes χHF, which not only improve accurate experimental determination of the Curie temperature but also provide a new magnetic method to estimate the order parameter for ilmenite–hematite solid solution samples.