Ferromagnetism in ferroelectric BaTiO3 induced by vacancies: Sensitive dependence on charge state, origin of magnetism, and temperature range of existence

Using density-functional calculations we investigate the possibility and underlying mechanism of generating ferromagnetism (FM) in ferroelectric ${\mathrm{BaTiO}}_{3}$ by native vacancies. For the same vacancy species but different charge states (e.g., ${\mathrm{V}}_{\mathrm{O}}^{0}$ vs ${\mathrm{V}}_{\mathrm{O}}^{2+}$), our paper reveals a marked difference in magnetic behaviors. For instance, while ${\mathrm{V}}_{\mathrm{O}}^{0}$ is ferromagnetic, ${\mathrm{V}}_{\mathrm{O}}^{2+}$ is not. This sensitive dependence, which has often been overlooked, highlights the critical importance of taking into account different charge states. Furthermore, while oxygen vacancies have been often used in experiments to explain the vacancy-induced FM, our calculation demonstrates that Ti vacancies, in particular ${\mathrm{V}}_{\mathrm{Ti}}^{3\ensuremath{-}}$ and ${\mathrm{V}}_{\mathrm{Ti}}^{2\ensuremath{-}}$ with low formation energies, generate even stronger ferromagnetism in ${\mathrm{BaTiO}}_{3}$, with a magnetic moment which is 400% larger than that of ${\mathrm{V}}_{\mathrm{O}}^{0}$. Interestingly, this strong FM of ${\mathrm{V}}_{\mathrm{Ti}}^{}$ can be further enhanced by hole doping. Although both cation vacancies (${\mathrm{V}}_{\mathrm{Ti}}^{\mathrm{q}}$) and anion vacancies (${\mathrm{V}}_{\mathrm{O}}^{0}$) induce FM, their mechanisms differ drastically. FM of anion vacancies originates from the spin-polarized electrons at Ti sites, but FM of cation vacancies stems from the spin-polarized holes at O sites. This paper also sheds light on vacancy-induced FM by discovering that the spin densities of all three considered vacancy species are highly extended in real space, distributed far away from the vacancy. Moreover, we predict that the ferromagnetism caused by ${\mathrm{V}}_{\mathrm{Ti}}^{3\ensuremath{-}}$ is able to survive at high temperatures, which is promising for room-temperature spintronic or multiferroic applications.