  We study Mn substitution for Ti in BaTiO3 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, 3d4 and 3d5.
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 is
closely fixed to the high spin 3d5 state. Here we show that inclusion of charge
and spin fluctuations is necessary to obtain an accurate ground state of
transition metal doped ferroelectrics.
