First-principles based Monte Carlo modeling of the magnetization of oxygen-deficient Fe-substituted SrTiO₃

Transition-metal (TM) substituted SrTiO₃ has attracted much attention because its magnetism and/or ferroelectricity can be tuned via cation substitution, point defects, strain and/or oxygen deficiency. For example, Goto et al. [Phys. Rev. Applied, 7, 024006 (2017)] reported the magnetization of SrTi_1-FeO_3- (STF) grown under different oxygen pressures and on various substrates. Here, we use hybrid density functional theory to calculate the effects of different oxygen vacancy (V_O) states in STF on the magnetization for a variety of Fe cation arrangements. The magnetic states of the cations associated with the V_O ground-states for x = {0.125, 0.25} are used within a Monte Carlo model for collinear magnetism to simulate the spontaneous magnetization. Our model captures several experimental features of STF, i.e., an increase in magnetization for small δ up to a maximum of ∼0.35μ_B per formula unit at an intermediate number of vacancies, with a slower decrease in magnetization with an increasing number of vacancies. Our approach gives insight into the relation between vacancy concentration and the oxygen pressure required to maximize the magnetization.