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.
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