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We study the Ruderman-Kittel-Kasuya-Yosida interaction in 3D Diracsemimetals. Using retarded Green's functions in real space, we obtain andanalyze asymptotic expressions for the interaction, with magnetic impurities atdifferent distances and relative angle with respect to high symmetry directionson the lattice. We show that the Fermi velocity anisotropy in these materialsproduces a strong renormalization of the magnitude of the interaction, as wellas a correction to the frequency of oscillation in real space. Hybridization ofthe impurities to different conduction electron orbitals are shown to result ininteresting anisotropic spin-spin interactions which can generate spiral spinstructures in doped samples.

Hybridization and anisotropy in the exchange interaction in 3D Dirac semimetals