Orbital isotropy of magnetic fluctuations in correlated electron materials induced by Hund's exchange coupling

TL;DR

This paper investigates how Hund's exchange coupling influences the spatial symmetry and orbital structure of magnetic fluctuations in correlated electron materials, revealing a transition from anisotropic to isotropic fluctuations driven by Hund's coupling.

Contribution

It develops a multi-orbital diagrammatic extension of dynamical mean field theory to analyze magnetic fluctuations in a three-orbital model, highlighting Hund's coupling as a key factor in orbital isotropy.

Findings

Hund's coupling governs the form of spatial spin fluctuations.

Large Hund's coupling induces orbital isotropy in magnetic fluctuations.

Orbital isotropy can be achieved at different electron fillings.

Abstract

Characterizing non-local magnetic fluctuations in materials with strong electronic Coulomb interactions remains one of the major outstanding challenges of modern condensed matter theory. In this work we address the spatial symmetry and orbital structure of magnetic fluctuations in perovskite materials. To this aim, we develop a consistent multi-orbital diagrammatic extension of dynamical mean field theory, which we apply to an anisotropic three-orbital model of cubic $t_{2g}$ symmetry. We find that the form of spatial spin fluctuations is governed by the local Hund's coupling. For small values of the coupling, magnetic fluctuations are anisotropic in orbital space, which reflects the symmetry of the considered $t_{2g}$ model. Large Hund's coupling enhances collective spin excitations, which mixes orbital and spatial degrees of freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this effect can be seen only in two-particle quantities; single-particle observables remain anisotropic for any value of the Hund's coupling. Importantly, we find that the orbital isotropy can be induced both, at half-filling and for the case of $4$ electrons per lattice site, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic modes, respectively.