Mn(IV) and Cr(III) impurities in cubicBaTiO3: Theoretical study through a molecular-orbital model

The self-consistent-field multiple-scattering Xα method is employed to calculate the electronic structure of substitutional trivalent chromium and tetravalent manganese ions in cubic ${\mathrm{BaTiO}}_3$. The energy levels are provided in both high- and low-spin configurations, while the electronic distributions are reported and discussed for the former only ${(}^4$ ${\mathrm{A}}_2$), which is found to be the ground term for the two ions. In particular, it is shown that the ${}_{}{}^2{}_{}{}^{}\mathrm{E}$ or ${}_{}{}^4{}_{}{}^{}\mathrm{T}_2^{}{}_{}{}^{}$ excited states of the ${\mathrm{Cr}}^{3+}$ ion should be unstable or metastable. Transition-state calculations are carried out to obtain the energies of optical transitions, which are compared to available experimental data on ${\mathrm{SrTiO}}_3$-like crystals. Moreover, the dependence of the g tensor on covalent bonding along the isoelectronic series ${\mathrm{Cr}}^{3+}$, ${\mathrm{Mn}}^{4+}$, and ${\mathrm{Fe}}^{5+}$ is analyzed from the Xα results.