Double exchange model for correlated electrons in systems with $t_{2g}$ orbital degeneracy

TL;DR

This paper develops a double exchange model for $t_{2g}$ orbital systems, revealing how weaker exchange interactions stabilize specific magnetic and orbital phases, aligning with experimental observations in doped vanadates.

Contribution

The paper introduces a double exchange model tailored for $t_{2g}$ orbitals and analyzes its magnetic and orbital phase stability using mean-field methods, highlighting differences from $e_g$ systems.

Findings

Stabilization of C-type antiferromagnetic metallic phase and orbital liquid state.

Agreement with experimental magnetic structures and orbital order collapse.

Contrast with $e_g$ orbital systems favoring ferromagnetism.

Abstract

We formulate the double exchange (DE) model for systems with $t_{2g}$ orbital degeneracy, relevant for hole-doped cubic vanadates. In the relevant regime of strong on-site Coulomb repulsion $U$ we solve the model using two distinct mean-field approximations: Hartree-Fock, and mean-field applied to the formulation of the model in the Kotliar-Ruckenstein slave boson representation. We show how, due to the relative weakness of the DE mechanism via $t_{2g}$ degenerate orbitals, the anisotropic C-type antiferromagnetic metallic phase and the orbital liquid state can be stabilized. This is contrasted with the DE mechanism via $e_g$ degenerate orbitals which stabilizes the ferromagnetic order in the hole-doped regime of manganites. The obtained results are in striking agreement with the observed magnetic structures and the collapse of the orbital order in the doped La$_{1-x}$Sr$_x$VO$_3$, Pr$_{1-x}$Ca$_x$VO$_3$ and Nd$_{1-x}$Sr$_x$VO$_3$.