Magnetic and orbital correlations in a two-site molecule

TL;DR

This study investigates how orbital degeneracy influences magnetic and orbital correlations in a two-site molecule, revealing the importance of Hund's coupling and the effects of crystal field splitting on ground state properties.

Contribution

It provides an exact analysis of a two-orbital, two-site molecule showing how degeneracy, Hund's coupling, and crystal field splitting affect magnetic and orbital correlations, challenging traditional rules.

Findings

Spin and orbital correlations have opposite signs at low temperature with degenerate orbitals.

Hund's exchange promotes ferromagnetic correlations, especially in $t_{2g}$ orbitals.

Finite crystal field splitting can alter ground state properties and violate Goodenough-Kanamori rules.

Abstract

We analyze the role of orbital degeneracy in possible magnetic and orbital instabilities by solving exactly a two-site molecule with two orbitals of either $e_g$ or $t_{2g}$ symmetry at quarter-filling. As a generic feature of both models one finds that the spin and orbital correlations have opposite signs in the low temperature regime when the orbitals are degenerate, in agreement with the Goodenough-Kanamori rules. While Hund's exchange coupling $J_H$ induces ferromagnetic spin correlations in both models, it is more efficient for $t_{2g}$ orbitals where the orbital quantum number is conserved along the hopping processes. We show that the ground state and finite temperature properties may change even qualitatively with increasing Coulomb interaction when the crystal field splitting of the two orbitals is finite, and the Goodenough-Kanamori rules may not be followed.