Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: Implication for the 5d transition metal oxides AOsO_4 (A = K, Rb, and Cs)

摘要

We report our theoretical predictions on the linear magnetoelectric (ME) effects originating from odd-parity multipoles associated with spontaneous spin and orbital ordering on a diamond structure. We derive a two-orbital model for d electrons in e_g orbitals by including the effective spin-orbit coupling which arises from the mixing between e_g and t_(2g) orbitals. We show that the model acquires a net antisymmetric spin-orbit coupling once staggered spin and orbital orders occur spontaneously. The staggered orders are accompanied by odd-parity multipoles: magnetic monopole, quadrupoles, and toroidal dipoles. We classify the types of the odd-parity multipoles according to the symmetry of the spin and orbital orders. Furthermore, by computing the ME tensor using the linear response theory, we show that the staggered orders induce a variety of the linear ME responses. We elaborate all possible ME responses for each staggered order, which are useful to identify the order parameter and to detect the odd-parity multipoles by measuring the ME effects. We also elucidate the effect of lowering symmetry by a tetragonal distortion, which leads to richer ME responses. The implications of our results are discussed for the 5d transition metal oxides, AOSO_4 (A = K, Rb, and Cs), in which the order parameters are not fully identified.