Portal de Periódicos da CAPES

Atomic-Scale Magnetic Toroidal Dipole under Odd-Parity Hybridization

2019; Physical Society of Japan; Volume: 88; Issue: 5 Linguagem: Inglês

10.7566/jpsj.88.054708

1347-4073

Megumi Yatsushiro, Satoru Hayami,

Magnetic properties of thin films

A magnetic toroidal dipole (MTD) is one of the fundamental constituents for inducing magnetoelectric effects in the absence of both spatial inversion and time-reversal symmetries. We report on a microscopic investigation of the atomic-scale MTD in solids by taking into account the orbital degree of freedom with a different parity. We construct an effective two-orbital d–f tight-binding model on a polar tetragonal system for describing the atomic-scale MTD, which is obtained by incorporating the atomic spin–orbit coupling and odd-parity hybridization. The effective model exhibits two types of MTDs: in-plane \(x,y\) components activated through spontaneous ferromagnetic ordering or an external magnetic field, and an out-of-plane z component activated by a spontaneous odd-parity hybridization without spin moments. We show that the intraorbital (interorbital) Coulomb interaction in multiorbital systems plays an important role in stabilizing the in-plane (out-of-plane) MTD orderings. We also examine the magnetoelectric effect under each MTD ordering by calculating a linear response tensor. We show that the odd-parity hybridization enhances the magnetoelectric effect for the in-plane MTDs, while it suppresses that for the out-of-plane MTD.