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.

Electric Ferro-Axial Moment as Nanometric Rotator and Source of Longitudinal Spin Current

“…Recently, an electric axiality, which has the opposite time-reversal parity to the magnetization, has attracted growing interest [46,47], since the direct observation of its electronic ordering termed as ferro-axial (or ferro-rotational) ordering in RbFe(MoO 4 ) 2 [48,49] and NiTiO 3 [49][50][51]. Owing to the different time-reversal parity, a ferro-axial ordered state exhibits qualitatively different physical phenomena from the conventional ferromagnetic ordering [52][53][54][55], such as antisymmetric thermopolarization [56], longitudinal spin current generation [57,58], and nonlinear transverse magnetization [59]. However, materials to be identified as ferro-axial ordering in experiments are much smaller than those as ferromagnetic ordering: Co 3 Nb 2 O 8 [60], CaMn 7 O 12 [61], Ca 5 Ir 3 O 12 [62][63][64][65], BaCoSiO 4 [66], K 2 Zr(PO 4 ) 2 [67], Na 2 Hf(BO 3 ) 2 [68], and Na-superionic conductors [69].…”

Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca$_5$Ir$_3$O$_{12}$

“…For example, the MT quadrupole (MTQ) gives rise to a symmetric spin splitting in the electronic band structure to generate the spin current even without relativistic spin-orbit coupling (SOC). [65][66][67][68] In addition, the ET dipole (ETD) and octupole induce unconventional transverse responses, [69][70][71] such as the antisymmetric thermopolarization. 72) However, candidate materials with even-parity toroidal multipoles have been rare compared to those with odd-parity ones; CaMn 7 O 12 , 73) RbFe(MoO 4 ) 2 , 74,75) and NiTiO 3 [75][76][77] are a few examples to possess the ETD in bulk and no materials with the MTQ have been recognized.…”