Ferroaxial moment induced by vortex spin texture

Abstract

The nature of an electric ferro-axial 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 ferro-axial moment depending on the helicity. By introducing a multipole description, we show that the ferro-axial 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 ferro-axial moment in the presence of the magnetic orderings with the magnetic monopole and magnetic toroidal dipole. Moreover, we specifically consider a multi-orbital model in a four-sublattice tetragonal system to demonstrate the ferro-axial moment induced by the vortex spin texture. We show that the ferro-axial 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 ferro-axial moment. We also apply the result to a magnetic skyrmion with a topologically-nontrivial spin texture and discuss candidate materials.

14 pages, 9 figures, 6 tables

References in corpus (42)

• Spin current and magneto-electric effect in non-collinear magnets
• Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet
• Cluster multipole theory for anomalous Hall effect in antiferromagnets
• Towards a microscopic theory of toroidal moments in bulk periodic crystals
• Electronic Orbital Currents and Polarization in Mott Insulators
• Gate-controllable magneto-optic Kerr effect in layered collinear antiferromagnets
• Toroidal order in metals without local inversion symmetry
• Optical Magnetoelectric Effect in Multiferroic Materials: Evidence for a Lorentz Force Acting on a Ray of Light
• Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets
• Observation of a ferro-rotational order coupled with second-order nonlinear optical fields
• Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2
• Square skyrmion crystal in centrosymmetric itinerant magnets
• Anomalous Hall effect in $\kappa$-type organic antiferromagnets
• Multipole expansion for magnetic structures: A generation scheme for symmetry-adapted orthonormal basis set in crystallographic point group
• Thermodynamically stable skyrmion lattice in tetragonal frustrated antiferromagnet with dipolar interaction
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Anomalous Hall resistivity and possible topological Hall effect in the EuAl${}_4$ antiferromagnet
• Zoology of multiple-Q spin textures in a centrosymmetric tetragonal magnet with itinerant electrons
• Complete Multipole Basis Set for Single-Centered Electron Systems
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Essential role of anisotropic magnetic dipole in anomalous Hall effect
• Multiple skyrmion crystal phases by itinerant frustration in centrosymmetric tetragonal magnets
• Degeneracy Lifting of Néel, Bloch, and Anti-Skyrmion Crystals in Centrosymmetric Tetragonal Systems
• Emergent spin-valley-orbital physics by spontaneous parity breaking
• Spontaneous multipole ordering by local parity mixing
• Manipulating magnetoelectric effect -- Essence learned from Co${}_4$Nb${}_2$O${}_9$
• Magnetic and transport anomalies in R2RhSi3 (R= Gd, Tb, and Dy), resembling those of an exotic magnetic skyrmion Gd2PdSi3
• Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: implication to 5$d$ transition metal oxides $A$OsO${}_4$ ($A=$ K, Rb, and Cs)
• Spin order and fluctuations in the EuAl${}_4$ and EuGa${}_4$ topological antiferromagnets: A $\mu$SR study
• Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling
• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Room temperature antiferromagnetic order in superconducting X_yFe_{2-x}Se_ 2, (X= Rb, K): a powder neutron diffraction study
• Mechanism of antisymmetric spin polarization in centrosymmetric multiple-$Q$ magnets based on bilinear and biquadratic spin cross products
• Spin reorientation in TlFe1.6Se2 with complete vacancy ordering
• Magnetic structure and multiferroicity of Sc-substituted hexagonal YbFeO${}_3$
• Essential model parameters for nonreciprocal magnons in multisublattice systems
• Crystal structure and the magnetic properties of the 5d transition metal oxide AOsO4 (A = K, Rb, Cs)
• Spin-orbital-momentum locking under odd-parity magnetic quadrupole ordering
• Nonreciprocal Transport in Noncoplanar Magnetic Systems without Spin-Orbit Coupling, Net Scalar Chirality, or Magnetization
• Atomic-Scale Magnetic Toroidal Dipole under Odd-Parity Hybridization