Effects of Manganese Addition on the Electronic Structure of BaTiO$_3$

Mn is used as a dopant to improve the electromechanical properties of perovskite oxides. We elucidate the role of Mn defects and associated vacancies on the electronic, atomic and ferroelectric properties of BaTiO$_3$. Using density functional theory (DFT) and DFT+U we investigate the equilibrium geometry and electronic properties of Mn ion on A or B sites and with compensating oxygen vacancies. We study the change in the oxidation state of Mn in response to local environment changes, such as the presence of oxygen vacancies.