Magnetic mean-field modeling of solid solutions: Theoretical foundations with application to the hematite-ilmenite system

Published

August 17, 2015

Author(s)

Karl Fabian, V P. Shcherbakov, S. McEnroe, P. Robinson, Benjamin P. Burton

Abstract

By rigorously deriving A spatially averaged mean-field model for fully or partially ordered members of the ilmenite-hematite solid solution series is rigorously derived from the Heisen-berg Hamiltonian by first assuming no temporal correlation of atomic spins, and then by spa-tially averaging over spins at equivalent atomic positions. The model is based on the geometry of exchange interactions between nearest and next-nearest neighbors and predicts magnetization curves in homogenous solid solutions with variable degree of order. While the presented general framework 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 improves accurate experimental determination of the Curie temperature, but also provides a new method to estimate the order parameter for ilmenite-hematite solid solution samples.

Citation

Geophysical Journal International

Pub Type

Journals

Keywords

Magnetic mineralogy and petrology, rock and mineral magnetismFe2O3, FeTiO3, hematite-ilmenite

Citation

Fabian, K. , Shcherbakov, V. , McEnroe, S. , Robinson, P. and Burton, B. (2015), Magnetic mean-field modeling of solid solutions: Theoretical foundations with application to the hematite-ilmenite system, Geophysical Journal International (Accessed October 11, 2025)