Uniform and Staggered electric axial moment in zigzag chain

TL;DR

This paper theoretically explores how electric axial moments can be induced and ordered in zigzag-chain systems with noncentrosymmetric structures, revealing new mechanisms for electric and magnetic orderings.

Contribution

It uncovers the role of local odd-parity hybridization and electric fields in inducing electric axial moments and their orderings in zigzag chains, extending understanding of such phenomena.

Findings

Staggered electric axial moment induced by external electric field

Uniform electric axial moment associated with staggered electric dipole order

Uniform electric quadrupole order accompanies the electric axial moment

Abstract

We theoretically investigate electronic orderings with the electric axial moment without breakings of both spatial inversion and time-reversal symmetries in the zigzag-chain system. Especially, we elucidate the role of the local odd-parity hybridization arising from locally noncentrosymmetric lattice structures based on symmetry and microscopic model analyses. We show that the odd-parity crystalline electric field gives rise to an effective cross-product coupling between the electric dipole and electric toroidal dipole, the latter of which corresponds to the electric axial moment. As a result, the staggered component of the electric axial moment is induced by applying an external electric field, while its uniform component is induced via the appearance of staggered electric dipole ordering. We also show that uniform electric quadrupole ordering accompanies uniform electric axial moment. Furthermore, we discuss transverse magnetization as a consequence of the orderings with the uniform electric axial moment. Our results extend the scope of materials exhibiting electric axial ordering to those with locally noncentrosymmetric lattice structures.