Investigation of the Effects of Strain and Electric Field on the Spin-State Energetics of Co-Doped BaTiO3 and PbTiO3

First principles investigations are performed to study the effect of in-plane strain and application of an electric field on the spin state energetics of cobalt doped ferroelectric perovskites, BaTiO₃ (BTO) and PbTiO₃ (PTO). The variation of strain has a large and systematic effect on the unit cell volume, and the spin splitting is clearly correlated with the volume, where increased volume favors the HS state. At equilibrium geometry, the local density approximation (LDA) favors the LS state, while the generalized-gradient approximation (GGA) favors the HS state. However, when using the experimental lattice parameters, the GGA also favors the LS. The more accurate HSE and r²SCAN functionals both favor the HS state, but for BTO, on application of a small in-plane compressive uniaxial strain of 2–3%, both the HS and LS states become degenerate in energy thus exhibiting bistable magnetism. Investigation of the magnetic anisotropy (including spin-orbit coupling) shows a change in the (001) to (010) direction of the spin easy axis from the tetragonal to orthorhombic structural phases of Co:PTO/Co:BTO. The application of an external electric field on a Co:PTO slab has a small effect on the magnetic and structural properties of the system.