Akane Inda

Chirality ubiquitously appears in nature; however, its quantification remains obscure owing to the lack of microscopic description at the quantum-mechanical level. We propose a way of evaluating chirality in terms of the electric toroidal monopole, a practical entity of time-reversal even pseudoscalar (parity-odd) objects reflecting relevant electronic wave functions. For this purpose, we analyze a twisted methane molecule at the quantum-mechanical level, showing that the electric toroidal monopoles become a quantitative indicator for chirality. In the twisted methane, we clarify that the handedness of chirality corresponds to the sign of the expectation value of the electric toroidal monopole and that the most important ingredient is the modulation of the spin-dependent imaginary hopping between the hydrogen atoms, while the relativistic spin–orbit coupling within the carbon atom is irrelevant for chirality.

Magnetic anisotropy is one of the important factors in determining magnetic structures. The type of magnetic anisotropy is closely related to the symmetry of crystals. We theoretically investigate magnetic anisotropy and its related magnetic instability arising from an electric axial moment, which appears under the breaking of the mirror symmetry parallel to the moment but does not require the breakings of both spatial inversion and time-reversal symmetries. By performing perturbation and mean-field calculations in a complementary way, we show the appearance of the in-plane magnetic anisotropy when the electric axial moment occurs, which tends to tilt in-plane spin moments from the crystal axes in collaboration with relativistic spin-orbit coupling. We demonstrate such a tendency for single-sublattice and four-site cluster models. In the four-site cluster model, we show that a spin configuration consisting of magnetic monopole and magnetic toroidal dipole tends to be realized in the region where a spin vortex is stabilized by the exchange interactions.