Ferroaxial moment induced by vortex spin texture

Abstract

The nature of an electric ferroaxial moment characterizing a time-reversal-even axial-vector quantity is theoretically investigated under magnetic orderings. We clarify that a vortex spin texture results in the emergence of the ferroaxial moment depending on the helicity. By introducing a multipole description, we show that the ferroaxial nature appears when two types of odd-parity magnetic multipoles become active under the vortex spin texture: One is the magnetic monopole and the other is the magnetic toroidal dipole. We present all the magnetic point groups to possess the ferroaxial moment in the presence of the magnetic orderings with the magnetic monopole and magnetic toroidal dipole. Moreover, we specifically consider a multiorbital model in a four-sublattice tetragonal system to demonstrate the ferroaxial moment induced by the vortex spin texture. We show that the ferroaxial moment is microscopically characterized by both the cluster-scale and atomic-scale axial-vector quantities: The former is described by the vortex of the local electric dipole and the latter is represented by the outer product of the local orbital and spin angular momenta. Moreover, we find that the atomic spin-orbit coupling and the hybridization between orbitals with different parity are key ingredients to induce the ferroaxial moment. We also apply the result to a magnetic skyrmion with a topologically nontrivial spin texture and discuss candidate materials.