Abstract
Ferrotoroidal order, which represents a spontaneous arrangement of toroidal moments, has recently been found in a few linear magnetoelectric materials. However, tuning toroidal moments in these materials is challenging. Here, we report switching between ferritoroidal and ferrotoroidal phases by a small magnetic field, in a chiral triangular-lattice magnet BaCoSiO4 with tri-spin vortices. Upon applying a magnetic field, we observe multi-stair metamagnetic transitions, characterized by equidistant steps in the net magnetic and toroidal moments. This highly unusual ferri-ferroic order appears to come as a result of an unusual hierarchy of frustrated isotropic exchange couplings revealed by first principle calculations, and the antisymmetric exchange interactions driven by the structural chirality. In contrast to the previously known toroidal materials identified via a linear magnetoelectric effect, BaCoSiO4 is a qualitatively new multiferroic with an unusual coupling between several different orders, and opens up new avenues for realizing easily tunable toroidal orders.
Highlights
Ferrotoroidal order, which represents a spontaneous arrangement of toroidal moments, has recently been found in a few linear magnetoelectric materials
Ferrotoroidicity, that is, the uniform arrangement of toroidal moments has been actively discussed as the fourth primary ferroic order, in addition to ferromagnetism, ferroelectricity, and ferroelasticity[2,3,4,5,6,7,8,9]
From the symmetry-allowed terms in the free energy expression, toroidal moments should lead to antisymmetric components in the linear magnetoelectric effect
Summary
Ferrotoroidal order, which represents a spontaneous arrangement of toroidal moments, has recently been found in a few linear magnetoelectric materials. It is worth noting that the observed signal in LiCoPO4 results from a staggered arrangement of toroidal moments, i.e., it is a ferri-(not ferro)toroidal order, related to the collinear magnetic structure with bi-spin vortices[15] Another case is pyroxene LiFeSi2O6, which shows a finite off-diagonal magnetoelectric effect[13]. The control of toroidal domains in this compound was only possible by applying crossed magnetic and electric fields, as revealed by the polarized neutron analysis This appears to be a common problem in these toroidal materials, which require simultaneous application of crossed magnetic and electric field, and is a consequence of symmetry constraints[12,13,14]. This restriction is directly related to their linear magnetoelectric effect, rendering these materials curious, but impractical
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