An approach is proposed for evaluating dipolar and multipolar inter-siteinteractions in strongly correlated materials. This approach is based on thesingle-site dynamical mean-field theory (DMFT) in conjunction with the atomicapproximation for the local self-energy. Starting from the local momentparamagnetic state described by DMFT we derive inter-site interactions byconsidering the response of the DMFT grand potential to small fluctuations ofatomic configurations on two neighboring sites. The present method is validatedby applying it to one-band and two-band e$_g$ Hubbard models on thesimple-cubic 3$d$ lattice. It is also applied to study the spin-orbital orderin the parent cubic structure of ternary chromium fluoride KCrF$_3$. We obtainthe onset of a G-type antiferro-orbital order at a significantly lowertemperature compared to that in real distorted KCrF$_3$. In contrast, itslayered A-type antiferromagnetic order and N\'eel temperature are rather wellreproduced. The calculated full Kugel-Khomskii Hamiltonian containsspin-orbital coupling terms inducing a misalignment in the antiferro-orbitalorder upon the onset of antiferromagnetism.
展开▼
