Polarizing Oxygen Vacancies in Insulating Metal Oxides under a High Electric Field

We demonstrate a thermodynamic formulation to quantify defect formation energetics in an insulator under a high electric field. As a model system, we analyzed neutral oxygen vacancies (color centers) in alkaline-earth-metal binary oxides using density functional theory, Berry phase calculations, and maximally localized Wannier functions. The work of polarization lowers the field-dependent electric Gibbs energy of formation of this defect. This is attributed mainly to the ease of polarizing the two electrons trapped in the vacant site, and secondarily to the defect induced reduction in bond stiffness and softening of phonon modes. The formulation and analysis have implications for understanding the behavior of insulating oxides in electronic, magnetic, catalytic, and electrocaloric devices under a high electric field.