Chirality in BaTiOCu$_4$(PO$_4$)$_4$

TL;DR

This study uses first principles calculations to analyze the ferrochiral phase transition in chiral BaTiOCu$_4$(PO$_4$)$_4$, identifying key multipole moments as order parameters and evaluating their effectiveness.

Contribution

It introduces a detailed analysis of atomic multipole moments as order parameters for chirality in BaTiOCu$_4$(PO$_4$)$_4$, advancing understanding of its phase transition.

Findings

Antiferroically ordered electric toroidal dipole moments serve as an order parameter.

The overall chiral order involves antipolar electric dipole and electric toroidal dipole moments.

Some proposed order parameters for chirality can be excluded based on the analysis.

Abstract

We present a first principles study of the ferrochiral phase transition in chiral BaTiOCu$_4$(PO$_4$)$_4$, which has been shown using X-ray diffraction to proceed via the antiferroaxial rotation of antipolar structural units. We analyze the atomic-site electric and magnetic multipole moments to identify connections between these multipoles and chirality and corroborate the previous experimental interpretation. We show that antiferroically ordered atomic-site electric toroidal dipole moments act as an order parameter for the antiferroaxial rotations, and that the overall chiral order is parameterized by the composite order of the antipolar electric dipole and electric toroidal dipole moments. Finally, we evaluate the suitability of various proposed order parameters for chirality, show that some can be excluded and suggest the most promising directions for future exploration.