Hidden Magnetic Toroidicity in Collinear Spins

A magnetic toroidal moment is the order parameter for ferro-toroidicity, playing a prominent role in condensed matter physics by its close ties to off-diagonal conductivity and non-reciprocal transport. This concept shows promise for applications in quantum computing devices and quantum communication protocols. Typically, a magnetic toroidal moment refers to the axial vector of a spin vortex, suggesting that collinear spins cannot host a toroidal moment parallel to the spins. However, in this talk, I will present the experimental observation of emergent out-of-plane magnetic toroidal moment in a triangular Co²⁺-based collinear antiferromagnet. The magnetic structure determined by single crystal and powder neutron diffraction exhibits an A-type collinear antiferromagnetic order with k = (0, 0, 0) on an R-3 crystallographic lattice. A significant magnetic toroidal moment is evidenced by a pronounced off-diagonal linear magnetoelectricity. Symmetry analysis reveals a scenario that a combination of a diagonal linear magnetoelectric sublattice plus a ferro-rotation type structural distortion gives rise to an effective magnetic toroidal moment. These results demonstrate a rare-earth-free magnetoelectric material with excellent performance, and that the symmetry analysis is a powerful tool in predicting emergent phenomena and designing functional quantum materials.