Calculation of the electronic structure, lattice dynamics, and optical and magnetic properties of europium tetraborate EuB$_{4}$O$_{7}$

The electronic band structure, lattice vibration frequencies, and optical and magnetic properties of EuB$_{4}$O$_{7}$ crystal with $\alpha$-SrB$_{4}$O$_{7}$-type structure are calculated within the density functional method. It is found that this compound is a dielectric with a band gap of the order of 4 eV. It is found that the ground state of this crystal is the state with ferromagnetic ordering of Eu$^{2+}$ spins. Exchange interaction constants are calculated; the ferromagnetic ordering temperature is estimated within the molecular field approximation ($T_{c}\approx$ 1 K). The EuB$_{4}$O$_{7}$ compound is a magnetic pyroelectric and, hence, can exhibit magnetoelectric properties. The calculated polarization change during ferromagnetic ordering of this crystal is 3973 $\mu$C/m$^2$.