Ferromagnetic Ferroelectricity due to Orbital Ordering

TL;DR

This paper proposes a design principle for creating ferromagnetic ferroelectric materials by activating orbital degrees of freedom, breaking inversion symmetry through antiferro orbital order, exemplified by VI3.

Contribution

It introduces a novel approach to realize ferromagnetic ferroelectricity via orbital ordering, providing specific design principles and identifying promising material candidates.

Findings

Orbital order can induce ferromagnetic and ferroelectric properties simultaneously.

VI3 is identified as a promising candidate for ferromagnetic ferroelectricity.

Design principles include non-centrosymmetric magnetic atoms and flexible orbitals in transition-metal compounds.

Abstract

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 $\mathcal{I}$. 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 $\mathcal{I}$, 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 $d^{2}$ configuration and relatively weak $d$-$p$ hybridization. Such a situation is realized in the van der Walls compound VI$_3$, which we expect to be ferromagnetic ferroelectric.