Two-site fluctuations and multipolar superexchange interactions in strongly correlated systems

TL;DR

This paper introduces a method combining DMFT and atomic approximation to evaluate inter-site multipolar interactions in strongly correlated materials, validated on Hubbard models and applied to study spin-orbital order in KCrF3.

Contribution

The paper develops a novel approach to calculate multipolar superexchange interactions using DMFT and atomic approximation, enabling analysis of complex spin-orbital phenomena.

Findings

Validated method on Hubbard models showing accurate inter-site interactions.

Reproduced magnetic and orbital ordering temperatures in KCrF3.

Derived a Kugel-Khomskii Hamiltonian with spin-orbital coupling effects.

Abstract

An approach is proposed for evaluating dipolar and multipolar inter-site interactions in strongly correlated materials. This approach is based on the single-site dynamical mean-field theory (DMFT) in conjunction with the atomic approximation for the local self-energy. Starting from the local moment paramagnetic state described by DMFT we derive inter-site interactions by considering the response of the DMFT grand potential to small fluctuations of atomic configurations on two neighboring sites. The present method is validated by applying it to one-band and two-band e$_g$ Hubbard models on the simple-cubic 3$d$ lattice. It is also applied to study the spin-orbital order in the parent cubic structure of ternary chromium fluoride KCrF$_3$. We obtain the onset of a G-type antiferro-orbital order at a significantly lower temperature compared to that in real distorted KCrF$_3$. In contrast, its layered A-type antiferromagnetic order and N\'eel temperature are rather well reproduced. The calculated full Kugel-Khomskii Hamiltonian contains spin-orbital coupling terms inducing a misalignment in the antiferro-orbital order upon the onset of antiferromagnetism.