  We study correlations and magnetic textures of localized spins, doped in
three-dimensional Dirac semimetals. An effective field theory for magnetic
moments is constructed by integrating out the fermionic degrees of freedom. The
spin correlation shows a strong anisotropy, originating from spin-momentum
locking of Dirac electrons, in addition to the conventional Heisenberg-like
ferromagnetic correlation. The anisotropic spin correlation allows
topologically nontrivial magnetic excitation textures such as a transient
hedgehog state, as well as the ferromagnetic ground state. The spin-wave
dispersion in ferromagnetic Weyl semimetal also becomes anisotropic, being less
dispersed perpendicular to the magnetization.
