First-principles based Monte Carlo modeling of the magnetization of oxygen-deficient Fe-substituted SrTiO 3

Transition-metal (TM) substituted SrTiO has attracted much attention because its magnetism and/or ferroelectricity can be tuned cation substitution, point defects, strain and/or oxygen deficiency. For example, Goto [ , , 024006 (2017)] reported the magnetization of SrTi Fe O (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 ) states in STF on the magnetization for a variety of Fe cation arrangements. The magnetic states of the cations associated with the V ground-states for = {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, , an increase in magnetization for small up to a maximum of ∼0.35 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.