The generalized method of quantitative description of the uniaxial anisotropy in weak ferromagnet rhombohedral calcite type structure crystals with S-state ions

The method for investigation of the uniaxial and hexagonal anisotropies in weakly ferromagnetic rhombohedral FeBO3 crystals with the Fe2+ magnetic impurity with the use of the single-ion and pair approximation has been developed. In the framework of this method, a quantitative discrepancy between theoretical and experimental data on a uniaxial field has been eliminated. The energy contributions to the hexagonal anisotropy that are caused by the Dzyaloshinsky–Moriya interaction, the crystal field of Fe3+ ions and the temperature dependence of this anisotropy were analytically treated. The experimental temperature dependence of the hexagonal anisotropy of FeBO3 crystals is explained. It is shown that the compensation point and the typical temperature dependence of the hexagonal anisotropy result from the competition of the contributions of Fe3+ and Fe2+ ions. It is shown that respective considerable contributions to the anisotropy of Fe3+ and Fe2+ ions are made by the cubic symmetry and the uniaxial symmetry of the exchange “single-ion” type. The anisotropy constants for FeBO3 crystal was obtained by using the described results. It was shown, that for the calcite type structure crystals (iron borate and manganese carbonate) with S-state ions, the single ion and pair models (which previously raised doubts in their validity and accuracy) describe the experimental data good enough. ► The method for investigation of the anisotropies in rhombohedral FeBO3 crystals has been developed. ► The energy contributions to the hexagonal anisotropy were analytically treated. ► The temperature dependence of the hexagonal anisotropy is analytically treated. ► The anisotropy constants for FeBO3 crystal was obtained by using of the obtained results.