Magnetic Properties of Fe₄BO₇ and Mn₄BO₇ Tetraborates in Three Structure Types

The crystal structure and magnetic properties of Fe₄BO₇ and Mn₄BO₇ tetraborates have been studied within DFT-GGA. The tetraborates can be found in several possible structural modifications. Three of them, namely, $Pbca$ (α-ZnB₄O₇), $Cmcm$ (β-ZnB₄O₇ structure type), and $P{{6}_{5}}22$ (γ-NiB₄O₇ structure type) have been considered here. The possible magnetic orderings in three structure types are described within group-theoretical analysis. The following DFT calculations allow finding the lowest energy magnetic structure for Fe₄BO₇ and Mn₄BO₇ in three structure types. The total energies of tetraborates in three structure types have been compared with and without taking into account the spin polarization. It has been found that Mn₄BO₇ and Fe₄BO₇ in the non-spin-polarized case have the α-ZnB₄O₇ and γ-NiB₄O₇ structure types as the lowest energy structure, respectively. However, when the magnetic structure is taken into account, the antiferromagnetic α-ZnB₄O₇ phase becomes the ground state for both tetraborates. The pressure dependence of the enthalpy of Fe₄BO₇ and Mn₄BO₇ tetraborates has been studied. It has been found that the applied pressure results in the appearance of the β-ZnB₄O₇ structure type as the lowest energy structure under pressure.