Magnetic, electronic, and optical properties of the tetraborates NiB$_{4}$O$_{7}$ and CoB$_{4}$O$_{7}$ in three structural modifications

Within a framework of the density functional theory using the VASP software package, physical properties of tetraborate compounds NiB$_{4}$O$_{7}$ and CoB$_{4}$O$_{7}$ in three structural modifications with space symmetry groups of $Pbca$, $Cmcm$ and $P6_5$22 were calculated. The dependences of the enthalpy of compounds on pressure in studied structural modifications are calculated. The calculated electron densities of states and band structures showed that studied compounds in all considered modifications are dielectrics with a band gap of 3–4 eV. The calculation of the magnetic exchange constants was carried out in the Heisenberg model, which showed qualitative agreement with experiment.