Symmetry constraints on the electrical polarization in novel multiferroic materials

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 $\text{k}$ with $\text{-k}$, 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.

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• Charge disproportionation and collinear magnetic order in the frustrated triangular antiferromagnet AgNiO2
• Manipulating the magnetic structure by electric fields in multiferroic ErMn2O5
• Effect of Inversion Symmetry on Incommensurate Order in Multiferroic RMn2O5, R=rare earth
• The incommensurate magnetic structure of YMn2O5: a stringent test of the multiferroic mechanism
• Induced ferroelectric phases in TbMn_2O_5
• The commensurate phase of multiferroic HoMn2O5 studied by X-ray magnetic scattering
• Order Parameters and Phase Diagram of Multiferroic RMn${}_2$O${}_5$
• Order Parameters and Phase Diagrams of Multiferroics
• Helical order and multiferroicity in the $S=1/2$ quasi-kagome system KCu${}_3$As${}_2$O${}_7$(OD)${}_3$
• Giant Magnetic Fluctuations at the Critical Endpoint in Insulating HoMnO3