Emergent cross-product-type spin-orbit coupling under ferroaxial ordering

TL;DR

This paper reveals how ferroaxial ordering induces a unique cross-product type spin-orbit coupling in transition metal oxides, driven by symmetry breaking and atomic interactions.

Contribution

It introduces a theoretical framework showing the emergence of cross-product spin-orbit coupling due to ferroaxial ordering in a tetragonal d-p cluster model.

Findings

Ferroaxial ordering breaks vertical mirror symmetry.

Emergent spin-orbit coupling has a cross-product form.

The phenomenon arises from atomic spin-orbit and d-p hybridization.

Abstract

A ferroic alignment of a time-reversal-even axial vector, which is called the ferroaxial ordered state, is identified by the spontaneous rotational distortion of the lattice structure to break the vertical mirror symmetry. We theoretically investigate what happens in the electronic structure once the ferroaxial ordering occurs by analyzing a tetragonal d-p cluster model with transition metal oxide in mind. By adopting the symmetry-adapted multipole representation, we elucidate the emergent cross-product form of the spin-orbit coupling by the interplay between the atomic spin-orbit coupling and the d-p hybridization according to the vertical mirror symmetry breaking, which corresponds to the electronic order parameter of the ferroaxial ordering.