Generalized Hund’s Rule for Two-Atom Systems

Abstract

Hund’s rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of theories on correlation is to provide a reliable way to describe the intermediate situation between the two limits. Here we propose an approach toward this goal, i.e., we study the two-atom systems of three $t_{2g}$ orbitals and see how the Hund’s rule is modified by the transfer integral t between them. It is found that the competition between t and the Hund’s coupling J at each atom determines the crossover from the molecular orbital limit to the strong correlation limit. Especially, our focus is on the generalization of the third rule about the spin-orbit interactions (SOIs), in the presence of the correlation. We have found that there are cases where the effective SOIs are appreciably enhanced by the Hund’s coupling at the filling of four or five electrons. This result provides a useful guideline to realize effectively strong SOI with common and lighter elements, which helps to realize nontrivial electronic states without heavy and rare elements.