  We study the Ruderman-Kittel-Kasuya-Yosida interaction in 3D Dirac
semimetals. Using retarded Green's functions in real space, we obtain and
analyze asymptotic expressions for the interaction, with magnetic impurities at
different distances and relative angle with respect to high symmetry directions
on the lattice. We show that the Fermi velocity anisotropy in these materials
produces a strong renormalization of the magnitude of the interaction, as well
as a correction to the frequency of oscillation in real space. Hybridization of
the impurities to different conduction electron orbitals are shown to result in
interesting anisotropic spin-spin interactions which can generate spiral spin
structures in doped samples.
