Basic aspects of ferroelectricity induced by noncollinear alignment of spins

I. V. Solovyev

doi:10.3390/condmat10020021

paper

Basic aspects of ferroelectricity induced by noncollinear alignment of spins

arXiv:2501.11970 · doi:10.3390/condmat10020021

Abstract

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 $I F = F$ and $IT A = A$ . 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 in the from $P = P_{12} [e_{1} \times e_{2}] + e_{1} Π e_{1} - e_{2} Π e_{2}$ . $P_{12}$ can be evaluated in the framework of superexchange theory, resulting in $P_{12} \sim r_{12}^{0}$ , where $r_{12}^{0}$ is the part of the position operator produced by the spin-orbit coupling. $r_{12}$ remains invariant under $I$ , explaining why noncollinear spins can induce $P$ even in the centrosymmetric case. The properties of $r_{12}$ are rationalized from the viewpoint of symmetry of the Kramers states. The Katsura-Nagaosa-Balatsky rule $P \propto ε_{21} \times [e_{1} \times e_{2}]$ ( $ε_{21}$ being the bond direction) 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. The properties of known multiferroics are reconsidered from the viewpoint of these principles.

20 pages, 12 figures

Basic aspects of ferroelectricity induced by noncollinear alignment of spins

Abstract

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