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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 Hunds 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 Hunds 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 Hunds coupling. Importantly, we find that the orbital isotropy can be induced both, at half-filling and for the case of 4/3 electrons per orbital, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic modes, respectively.
We study the doping-driven Mott metal-insulator transition for multi-orbital Hubbard models with Hunds exchange coupling at finite temperatures. As in the single-orbital Hubbard model, the transition is of first-order within dynamical mean field theo
The Dzyaloshinskii-Moriya (DM) interaction, as well as symmetric anisotropic exchange, are important ingredients for stabilizing topologically non-trivial magnetic textures, such as, e.g., skyrmions, merons and hopfions. These types of textures are c
We point out the generic competition between the Hunds coupling and the spin-orbit coupling in correlated materials, and this competition leads to an electronic dilemma between the Hunds metal and the relativistic insulators. Hunds metals refer to th
We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations w
Antiferromagnetism (AF) such as Neel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Neel AF ordering in 2D can be dominantly induced by electron-phonon couplings (EPC) has