Nonlinear Transverse Magnetic Susceptibility under Electric Toroidal Dipole Ordering

Abstract

An electric toroidal dipole (ETD) moment is one of the fundamental dipole moments as well as electric and magnetic ones. Although it directly couples to neither an electric nor magnetic field due to its spatial inversion and time-reversal parities, its ordered state leads to unconventional transverse responses of the conjugate physical quantities. We here theoretically investigate nonlinear transverse magnetic susceptibility under the ETD ordering. By performing a self-consistent mean-field calculation for a five $d$-orbital model under a tetragonal crystalline electric field and using the nonlinear Kubo formula, we show that a third-order transverse magnetic susceptibility corresponding to a uniform magnetization perpendicular to the external magnetic field becomes nonzero once the ETD moment is ordered under tetragonal crystalline electric field. Moreover, we find that spin-orbital entanglement and a low-lying first excited crystal-field level are important for realizing large transverse responses.

5 pages with 4 figures

References in corpus (5)

• Observation of a ferro-rotational order coupled with second-order nonlinear optical fields
• Complete Multipole Basis Set for Single-Centered Electron Systems
• Symmetry analysis of current-induced switching of antiferromagnets
• Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca${}_5$Ir${}_3$O${}_{12}$
• Ferroaxial moment induced by vortex spin texture

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