Symmetry Analysis of Spin-Dependent Electric Dipole and Its Application to Magnetoelectric Effects

Abstract

Spin-dependent electric dipole operators are investigated group-theoretically for the emergence of an electric dipole induced by a single spin or by two spins, where the spin dependences are completely classified up to the quadratic order. For a single spin, a product of spin operators behaves as an even-parity electric quadrupole operator, which differs from an odd-parity electric dipole. The lack of the inversion symmetry allows the even-and odd-parity mixing, which leads to the electric dipole described by the electric quadruple operators. Point-group tables are given for classification of the possible spin-dependent electric dipoles and for the qualitative analysis of multiferroic properties, such as an emergent electric dipole moment coexisting with a magnetic moment, electromagnon excitation, and directional dichroism. The results can be applied to a magnetic ion in crystals or embedded in molecules at a site without the inversion symmetry. In the presence of an inversion symmetry, the electric dipole does not appear for a single spin. This is not the case for the electric dipole induced by two spins with antisymmetric spin dependence, which is known as vector spin chirality, in the presence of the inversion center between the two spins. In the absence of the inversion center, symmetric spin-dependent electric dipoles are also relevant. The detailed analysis of various symmetries of two-spin states is applied to spin dimer systems and the related multiferroic properties.

Antisymmetric Spin–Orbit Coupling Effect on Kondo-Induced Electric Polarization in a Triangular Triple Quantum Dot

“…Recently, we have reported a group-theoretical study of various spin-dependent electric dipoles in the absence of the inversion symmetry, including the relationship between the vector spin chirality of the two-site spins and possible electric dipoles induced by a magnetic field or magnetic ordering. 67) As another magnetoelectric effect, it will also be intriguing to reveal the interplay between the KIEP δn * and the vector spin chirality generated by the ASO-coupled spins in the present model. A detailed analysis is left for a future study.…”

First ESR Detection of Higgs Amplitude Mode and Analysis with Extended Spin-Wave Theory in Dimer System KCuCl$$_3$$

“…When there is no inversion center in a dimer, even and odd parities are not distinguishable. The electric dipole is then also described by symmetric operators such as S α l S β r +S β l S α r , where the coefficient tensor for this was classified by the symmetries in a dimer [67].…”

Theory of electronic magnetoelectric coupling in d5 Mott insulators

“…5(b) because the pseudospin 1/2 are not well defined for ∆ < 0 when λ = 0 (the local ground state is fourfold degenerate). (14) and (37) for the edge-sharing geometry in the JH /U → 0 limit (and λ/U → 0 for A1). The CF is included through HCF but the displacement of the ligands is neglected.…”

“…Coupling coefficients defined in Eqs. (17) and (37) for the corner-sharing geometry in the JH /U → 0 limit. The CF is included through HCF but the displacement of the ligands is neglected…”