Itinerant ferromagnetism in the oxygen-deficient EuTiO$_3$: A first-principles investigation

Effects of oxygen vacancy on the electronic structure and magnetism in the quantum paraelectric EuTiO$_{3}$ were investigated from first-principles. In contrast to antiferromagnetism in the pristine EuTiO$_{3}$, itinerant ferromagnetism was revealed in the oxygen-deficient EuTiO$_{3}$. The origin lies in the spin-polarized Ti 3$d$ states, which mediate a ferromagnetic exchange interaction between almost localized Eu 4$f$ spins. In addition, this ferromagnetic exchange coupling was strengthened via the partial occupation of Eu $5d$ states. These findings not only explain the observation of ferromagnetism in the unstrained EuTiO$_{3}$ thin films, but also demonstrate the potential application of EuTiO$_{3}$ in magnetoelectronics.