  We theoretically demonstrate the Ruderman-Kittel-Kasuya-Yosida interaction
between magnetic impurities that is mediated by the Weyl fermions embedded
inside a three-dimensional Weyl semimetal (WSM). The WSM is characterized by a
pair of Weyl points separated in the momentum space. Using the Green's function
method and a two-band model, we show that four terms contribute to the magnetic
impurity interaction in the WSM phase: the Heisenberg, Dzyaloshinsky-Moriya,
spin-frustrated and Ising terms. Except the last term which is vanishingly
small in the plane perpendicular to the line connecting two Weyl points, all
the other interaction terms are finite. Furthermore, the magnetic spins of the
Dzyaloshinsky-Moriya and spin-frustrated terms lie in the plane perpendicular
to the line connecting two Weyl points, but in this plane, the magnetic spins
of the Ising term have no components. For each contribution, an analytical
expression is obtained, falling off with a spatial dependence as $R^{-5}$ at
Weyl points and showing beating behavior that depends on the direction between
two magnetic impurities.
