Numerical study of t2g orbital system with ferromagnetic polarization

TL;DR

This study uses quantum Monte Carlo simulations to explore the orbital states in a ferromagnetic Mott insulator with t2g orbitals, revealing no clear orbital order but indicating a gap-like behavior in susceptibility.

Contribution

It provides the first numerical analysis of finite temperature orbital states in a ferromagnetic t2g system using quantum Monte Carlo methods.

Findings

No significant staggered orbital order observed.

Orbital gap-like behavior detected in susceptibility.

Threshold behavior in correlation functions with Ising interaction.

Abstract

Finite temperature orbital state in a ferromagnetic Mott insulator with triply-degenerate $t_{2g}$ orbital is investigated numerically. We employ the quantum Monte Carlo simulation with the loop algorithm. Indications for conventional staggered-type orbital order are not remarkable down to the lowest temperature to which the present simulation can get access. Physical parameters monitoring the off-diagonal orbital order, which is characterized by a linear combination of the $(d_{yz}, d_{zx}, d_{xy})$ orbital-wave functions with equal weights, are not conspicuous. It is found that a orbital gap-like behavior appears in the uniform orbital susceptibility. This is supported by a threshold behavior in the staggered correlation function in a calculation with the additional Ising-type interaction. Some rigorous remarks for the long-range orbital order are also presented.