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Realization of ferromagnetic ferroelectricity, combining two ferroic orders in a single phase, is the longstanding problem of great practical importance. One of the difficulties is that ferromagnetism alone cannot break inversion symmetry. Therefore, such a phase cannon be obtained by purely magnetic means. Here, we show how it can be designed by making orbital degrees of freedom active. The idea can be traced back to a basic principle of interatomic exchange, which states that an alternation of occupied orbitals along a bond (i.e., antiferro orbital order) favors ferromagnetic coupling. Moreover, the antiferro orbital order breaks the inversion symmetry, so that the bond becomes not simply ferromagnetic but also ferroelectric. Then, we formulate main principles governing the realization of such a state in solids, namely: (i) The magnetic atoms should not be located in inversion centers, as in the honeycomb lattice; (ii) The orbitals should be flexible enough to adjust they shape and minimize the energy of exchange interactions; (iii) This flexibility can be achieved by intraatomic interactions, which are responsible for Hund's second rule and compete with the crystal field splitting; (iv) For octahedrally coordinated transition-metal compounds, the most promising candidates appear to be iodides with a d2 configuration and relatively weak d–p hybridization. Such a situation is realized in the van der Walls compound VI3, which we expect to be ferromagnetic ferroelectric.

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• Creative Commons BY Attribution 4.0 International
  

Keyword: ferroelectricity, ferromagnetism, orbital ordering, Hund’s rules

Date published: 2026-04-24

Publisher: IOP Publishing

Journal:

• JOURNAL OF PHYSICS-CONDENSED MATTER (ISSN: 09538984) vol. 38 issue. 16

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

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First published URL: https://doi.org/10.1088/1361-648X/ae5e14

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Updated at: 2026-04-21 11:15:26 +0900

Published on MDR: 2026-04-21 12:26:09 +0900