Symmetry constraints on the electrical polarization in multiferroic materials

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P. G. Radaelli^1,2 and L. C. Chapon¹
¹ISIS Facility, Rutherford Appleton Laboratory-CCLRC, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom
²Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

Received 6 September 2006; revised 17 May 2007; published 14 August 2007

Thesymmetry conditions for the development of a macroscopic electrical polarizationas a secondary order parameter to a magnetic ordering transitionand the constraints on the direction of the polarization vectorare determined by a nonconventional application of the theory ofirreducible corepresentations. In our approach, which is suitable for bothmagnetic and structural modulations, antiunitary operators are employed to describesymmetry operations that exchange the propagation vector k with −k,rather than operations combined with time reversal as in classicalcorepresentation analysis. Unlike the conventional irreducible representations, corepresentations can capturethe full symmetry properties of the system even if thepropagation vector is in the interior of the Brillouin zone.It is shown that ferroelectricity can develop even for acompletely collinear structure, and that helical and cycloidal magnetic structuresare not always polar. In some cases, symmetry allows thedevelopment of polarization parallel to the magnetic propagation vector. Ouranalysis also highlights the unique importance of magnetic commensurability, enablingone to derive the different symmetry properties of equivalent commensurateand incommensurate phases even for a completely generic propagation vector.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.76.054428
DOI:	10.1103/PhysRevB.76.054428
PACS:	77.80.-e; 75.25.+z; 61.50.Ah; 73.22.Gk 77.80.-e Ferroelectricity and antiferroelectricity 75.25.+z Spin arrangements in magnetically ordered materials including neutron and spin-polarized electron studies, synchrotron-source X-ray scattering, etc 61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling 73.22.Gk Broken symmetry phases (nanoscale materials) YEAR: 2007
KEYWORDS:	dielectric polarisation, ferroelectricity, magnetic structure, multiferroics

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