Antisymmetric Spin-Orbit Coupling in a d-p Model on a Zigzag Chain

We theoretically investigate how an antisymmetric spin-orbit coupling emerges in electrons moving on lattice structures which are centrosymmetric but break the spatial inversion symme- try at atomic positions. We construct an effective d-p model on the simplest lattice structure, a zigzag chain of edge-sharing octahedra, with taking into account the crystalline electric field, the spin-orbit coupling, and on-site and inter-site d-p hybridizations. We show that an effective antisymmetric spin-orbit coupling arises in the sublattice-dependent form, which results in a hidden spin polarization in the band structure. We explicitly derive the effective antisymmetric spin-orbit coupling for d electrons, which not only explains the hidden spin polarization but also indicates how to enhance it.