First-principles rationalization of self-reduction and lanthanide defect levels in SrB4O7

The ``abnormal'' self-reduction of several trivalent lanthanides in borates has been reported for a couple of decades, especially in ${\mathrm{SrB}}_{4}{\mathrm{O}}_{7}$, but only a phenomenological explanation has been given. Our calculations of the formation energies of lanthanide-doped and intrinsic defects in ${\mathrm{SrB}}_{4}{\mathrm{O}}_{7}$ provide an explanation for the mechanisms of self-reduction phenomena. Furthermore, we also give the trends of the $4f$ and $5d$ host referred binding energies of divalent lanthanides, which well fits and supports the result based on the extrapolation of the experimental data with the semiempirical chemical shift model [P. Dorenbos, Phys. Rev. B 85, 165107 (2012)]. Our results show that the calculations based on the supercell method by employing the projector augmented wave pseudopotentials are capable of interpreting the reduction and charge-transfer phenomena, and can provide a basis for the design of lanthanide-doped optical materials.