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Basic principles of ferroelectric activity induced by the noncollinear spins are reviewed. There is a fundamental reason why the inversion symmetry can be broken by magnetic order. Such situation occurs when the magnetic order simultaneously involves ferromagnetic (F) and antiferromagnetic (A) patterns, transforming under the spatial inversion I and time reversal T as IF=F and ITA=A, respectively. The incompatibility of these two conditions breaks the inversion symmetry, imposing a constraint on possible dependencies of polarization on directions of spins, which can include only antisymmetric coupling and single-ion anisotropy. The antisymmetric coupling (P12) can be evaluated in the framework of superexchange theory, resulting in P12~r12, where r12 is the part of the position operator induced by the relativistic spin-orbit coupling. r12 remains invariant under the spatial inversion, explaining why noncollinear spins can induce the electric polarization even in the centrosymmetric crystals. The properties of r12 are rationalized from the viewpoint of symmetry of the Kramers states. It is shown that the commonly used Katsura-Nagaosa-Balatsky rule is justified only for relatively high symmetry. The single-ion anisotropy vanishes for the spin 1/2 or if magnetic ions are located in the inversion centers, thus severely restricting the applicability of this microscopic mechanism. The properties of multiferroic materials are reconsidered from the viewpoint of these principles.

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• Creative Commons BY Attribution 4.0 International
  This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

Keyword: multiferroics, Mott insulators, noncollinear magnets, electric polarization, magnetoelectric effect, spin-orbit coupling, Wannier function methods

Date published: 2025-04-11

Publisher: MDPI

Journal:

• CONDENSED MATTER (ISSN: 24103896) vol. 10 issue. 2 p. 1-29

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Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.3390/condmat10020021

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Updated at: 2025-04-16 16:30:25 +0900

Published on MDR: 2025-04-16 14:29:35 +0900