  We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction
between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find
that the internode process, as well as the unique three-dimensional
spin-momentum locking, has significant influences on the RKKY interaction,
resulting in both a Heisenberg and an Ising term, and an additional
Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These
interactions can lead to rich spin textures and possible ferromagnetism in
Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic
Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results
provide an alternative scheme to engineer topological SMs and shed new light on
the application of Dirac and Weyl SMs in spintronics.
