Controlling magnetocrystalline anisotropy energies of magnetic dopants in ferroelectric oxides via local crystal-field tuning*

To date, most work on combining and controlling magnetism with ferroelectric distortions has been in systems with long-range order for both. Here instead, we create a magnetoelastic material with long-range electric order but localized magnetic order by doping a ferroelectric material with dilute amounts of magnetic ions. The crystal structure of the ferroelectric host is controllable by external electric fields, which can then change the local crystal field environment around the magnetic defect. The spin orientation of the defect is coupled to the local crystal field environment via the spin-orbit interaction. This offers a pathway to control the magnetic properties with an external electric field. Presently, there is no clear understanding of which crystal field environments will allow for favorable magnetic properties, such as reorientation  of the spin easy-axis with a 180-degree reversal of the electric polarization, or high magnetocrystalline anisotropy energies (MCAE). To address this, we consider the tetragonal, rhombohedral, and orthorhombic phases of prototypical ferroelectric oxide BaTiO₃ doped with Fe³⁺. We explore how the MCAE surfaces for these systems depend on crystalline symmetries and electronic structure through first-principles density functional theory (DFT) calculations and propose design principles for tailoring the electric control of single spin sites in ferroelectric oxide hosts.