Phase-field simulation on the interaction of oxygen vacancies with charged and neutral domain walls in hexagonal YMnO₃

A three-dimensional model of the interaction between the charged or neutral domain walls and oxygen vacancies in the hexagonal manganite YMnO₃ was proposed, and simulated using Landau-Ginzburg-Devonshire (LGD) theory, dynamic diffusion equation and Maxwell’s equation. The calculation proves that stiffness anisotropic factors can adjust the domain wall state and ultimately affect the distribution of oxygen vacancies. The head-to-head domain wall corresponds to low oxygen vacancy density, and the tail-to-tail domain wall corresponds to high oxygen vacancy density. The electrostatic field generated by the bound charge is the key factor leading to the change of oxygen vacancy distribution. Finally, e-index law N _d = ae ^b*dP/dz can fit the relationship between the oxygen vacancy concentration and the polarization gradient along z direction.