A linear-quadratic order parameter coupling model for magnetoelastic phase transitions in Fe1−xO and MnO

The combined structural and antiferromagnetic phase transition in wüstite, Fe1−xO, at the Néel temperature, TN ~ 195 K, is treated in terms of coupling between two macroscopic order parameters related to separate discrete instabilities. These each couple with a rhombohedral shear strain to give an indirect mechanism of linear (structural)–quadratic (magnetic) coupling between them. Based on patterns of lattice parameter and magnetic ordering data from the literature, it appears that the overall behaviour matches the general pattern of linear-quadratic coupling for a system with two rather similar instability temperatures. At low pressures, the magnetic instability occurs at a higher temperature than the structural instability but the coupling results in a single phase transition dominated by the influence of the magnetic order parameter. For Fe0.99O the magnetic order parameter, m, varies with temperature as ~m8 ∝ (TN − T), while for Fe0.94O the temperature dependence is of ~m4 or ~m2. It is proposed that, with increasing pressure, there is a crossover of instability temperatures such that the structural instability occurs first at pressures above ~13 GPa. This would be expected to give rise to a first-order phase transition, as appears to occur, but magnetic ordering would still occur simultaneously if the coupling is sufficiently strong. Symmetry analysis and comparison with the behaviour of MnO shows that there are a number of different possible magnetically ordered structures which could be stabilized by pressure or non-hydrostatic stress to give topologically rich phase diagrams