Magnetic properties of $\mathrm{FeB}_4\mathrm{O}_7$ and $\mathrm{MnB}_4\mathrm{O}_7$ tetraborates in three structure types

The crystal structure and magnetic properties of $\mathrm{FeB}_4\mathrm{O}_7$ and $\mathrm{MnB}_4\mathrm{O}_7$ tetraborates have been studied within DFT-GGA. The tetraborates can be found in several possible structural modifications. Three of them, namely, $Pbca$ ($\alpha$-$\mathrm{ZnB_4O_7}$), $Cmcm$ ($\beta$-$\mathrm{ZnB_4O_7}$ structure type), and $P6_522$ ($\gamma$-$\mathrm{NiB_4O_7}$ 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 $\mathrm{FeB}_4\mathrm{O}_7$ and $\mathrm{MnB}_4\mathrm{O}_7$ 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 $\mathrm{MnB}_4\mathrm{O}_7$ and $\mathrm{FeB}_4\mathrm{O}_7$ in the non-spin-polarized case have the $\alpha$-$\mathrm{ZnB_4O_7}$ and $\gamma$-$\mathrm{NiB_4O_7}$ structure types as the lowest energy structure, respectively. However, when the magnetic structure is taken into account, the antiferromagnetic $\alpha$-$\mathrm{ZnB_4O_7}$ phase becomes the ground state for both tetraborates. The pressure dependence of the enthalpy of $\mathrm{FeB}_4\mathrm{O}_7$ and $\mathrm{MnB}_4\mathrm{O}_7$ tetraborates has been studied. It has been found that the applied pressure results in the appearance of the $\beta$-$\mathrm{ZnB_4O_7}$ structure type as the lowest energy structure under pressure.