Primary ferrotoroidicity in antiferromagnets

Abstract

Antiferromagnetic ordering does not give rise to a measurable macroscopic symmetry-breaking order parameter such as the magnetization in a ferromagnet. An exception is the case of antiferromagnets with a vortexlike toroidal alignment of the magnetic moments in the unit cell because this gives rise to the formation of a spontaneous macroscopic toroidal moment which can be measured as a magnetoelectric effect. It is a long-standing question whether the toroidal moment is merely a side effect of the antiferromagnetic state or whether it can become the primary order parameter in a ferroic phase transition. Here we report the magnetoelectric properties of ${\mathrm{LiFeSi}}_{2}{\mathrm{O}}_{6}$ and show that they point to the role of the toroidal vector moment as the primary order parameter. Based on Landau theory we distinguish it from primary antiferromagnetic order. We thus justify the proposal that along with ferromagnets, ferroelectrics, and ferroelastics the ferrotoroidics constitute a new class of primary ferroics.