title: Ferroic nature of magnetic toroidal order.
abstract: Electric dipoles and ferroelectricity violate spatial inversion symmetry, and magnetic dipoles and ferromagnetism break time-inversion symmetry. Breaking both symmetries favours magnetoelectric charge-spin coupling effects of enormous interest, such as multiferroics, skyrmions, polar superconductors, topological insulators or dynamic phenomena such as electromagnons. Extending the rationale, a novel type of ferroic order violating space- and time-inversion symmetry with a single order parameter should exist. This existence is fundamental and the inherent magnetoelectric coupling is technologically interesting. A uniform alignment of magnetic vortices, called ferrotoroidicity, was proposed to represent this state. Here we demonstrate that the magnetic vortex pattern identified in LiCoPO4 exhibits the indispensable hallmark of such a ferroic state, namely hysteretic poling of ferrotoroidic domains in the conjugate toroidal field, along with a distinction of toroidal from non-toroidal poling effects. This consolidates ferrotoroidicity as fourth form of ferroic order.
authors.affiliation: HISKP, Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany.
authors.forename: Anne S
authors.initials: AS
authors.lastname: Zimmermann
authors.affiliation: Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093 Zurich, Switzerland.
authors.forename: Dennis
authors.initials: D
authors.lastname: Meier
authors.affiliation: Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093 Zurich, Switzerland.
authors.forename: Manfred
authors.initials: M
authors.lastname: Fiebig