pISSN 0374-4914 eISSN 2289-0041

## Research Paper

New Phys.: Sae Mulli 2021; 71: 645-651

Published online August 31, 2021 https://doi.org/10.3938/NPSM.71.645

## Competition Between Spin-orbit Coupling and Hund's Coupling in $t_{2g}^5$

Ara GO*

Department of Physics, Chonnam National University, Gwangju 61186, Korea

Correspondence to:arago@jnu.ac.kr

Received: May 6, 2021; Revised: July 12, 2021; Accepted: July 12, 2021

### Abstract

The effective angular momentum $j_{eff}$ efficiently describes the $t_{2g}^5$ orbitals in the presence of spin-orbit coupling. On the other hand, the $d$-orbital is spatially localized, and the local electrons have strong mutual two-body interactions, which play an important role in the metal-insulator transitions in transition-metal compounds. For a rotationally invariant $d$-orbital, the local interactions between electrons are expressed in terms of the local Coulomb interaction $U$ and Hund's coupling $J_H$. The Coulomb interaction prevents electrons from gathering at the same position, and Hund's coupling distributes the electron to maximize the spin and the orbital angular momenta. The Hund's coupling often competes against spin-orbit coupling. We explain both the competition between spin-orbit coupling and local interactions in the $t_{2g}^5$ orbital via an atomic limit description and the way in which the effects can be revealed in the electronic structure by dynamical mean-field calculation for a simplified lattice Hamiltonian.

Keywords: Metal-insulator transition, Spin-orbit coupling, Hund's coupling