Spin-polarized Flexoelectricity

Flexoelectricity describes the coupling between electric polarization and a strain gradient. First-principles methods for calculating flexoelectric tensor components have been previously developed that involve calculating electronic and lattice contributions using various charge-moment and force tensors. In magnetic materials, these charge moments can be spin-polarized – that is, the densities of spin up and down electrons can respond differently to atomic displacement. Based on this principle, we developed a method for calculating spin-polarized flexoelectric tensor components. We apply our method to a ferromagnetic oxide finding a sizeable spin-polarization of the flexoelectric tensor. Furthermore, we calculate its three independent flexoelectric tensor components and use these to predict an effective spin-polarized beam-bending flexoelectric constant along the (100) direction. The potential applications to spintronics through a metal-oxide interface is discussed.