Symmetry constraints on the electrical polarization in novel multiferroic materials

TL;DR

This paper uses a novel symmetry analysis based on irreducible co-representations to determine conditions for electrical polarization in multiferroic materials, revealing new insights into how magnetic structures influence ferroelectricity.

Contribution

It introduces a new application of co-representations employing anti-unitary operators to analyze symmetry constraints on polarization in magnetic and structural modulations.

Findings

Ferroelectricity can occur in collinear magnetic structures.

Helical and cycloidal magnetic structures are not always polar.

Symmetry can allow polarization parallel to magnetic propagation vector.

Abstract

The symmetry conditions for the development of a macroscopic electrical polarization as a secondary order parameter to a magnetic ordering transition, and the constraints on the direction of the polarization vector, are determined by a non-conventional application of the theory of irreducible co-representations. In our approach, which is suitable for both magnetic and structural modulations, anti-unitary operators are employed to describe symmetry operations that exchange the propagation vector $\textbf{k}$ with $\textbf{-k}$, rather than operations combined with time-reversal as in classical \textit{corep} analysis. Unlike the conventional irreducible representations, co-representations can capture the full symmetry properties of the system even if the propagation vector is in the interior of the Brillouin zone. It is shown that ferroelectricity can develop even for a completely collinear structure, and that helical and cycloidal magnetic structures are not always polar. In some cases, symmetry allows the development of polarization parallel to the magnetic propagation vector. Our analysis also highlights the unique importance of magnetic commensurability, enabling one to derive the different symmetry properties of equivalent commensurate and incommensurate phases even for a completely generic propagation vector.