Effective hexagonal magnetic anisotropy of hematite: Accounting for higher-order invariants

The contribution caused by hydrostatic pressure to the basal magnetic anisotropy of a rhombohedral easy-plane weak ferromagnet has been calculated based on the thermodynamic potential including new magnetoelastic invariants. It has been shown that, taking into account the magnetoelastic terms of a higher order with respect to the magnetic variables, it is possible to simulate the observed substantial increase in the effective hexagonal anisotropy constant in a strained hematite crystal by the action of a relatively weak hydrostatic pressure. This approach enables one to obtain additional terms proportional to the pressure in the cubic and hexagonal anisotropies. The contribution of new terms into the effective hexagonal anisotropy is substantially greater than the contribution from the previously considered addition to the uniaxial anisotropy constant. Estimates of higher-order magnetoelastic constants for hematite are presented.