Valence and spin fluctuations in the Mn-doped ferroelectric BaTiO3

We study Mn substitution for Ti in ${\mathrm{BaTiO}}₃$ with and without compensating oxygen vacancies using density functional theory (DFT) in combination with dynamical mean-field theory (DMFT). We find strong charge and spin fluctuations. Without compensating oxygen vacancies, the ground state is found to be a quantum superposition of two distinct atomic valences, $3{d}⁴$ and $3{d}⁵$. Introducing a compensating oxygen vacancy at a neighboring site reduces both charge and spin fluctuations due to the reduction of electron hopping from Mn to its ligands. As a consequence, valence fluctuations are reduced, and the valence is closely fixed to the high spin $3{d}⁵$ state. Here we show that inclusion of charge and spin fluctuations is necessary to obtain an accurate ground state of transition metal-doped ferroelectrics.