  We theoretically study the spin susceptibility of Dirac semimetals using the
linear response theory. The spin susceptibility is decomposed into an intraband
contribution and an interband contribution. We obtain analytical expressions
for the intraband and interband contributions of massless Dirac fermions. The
spin susceptibility is independent of the Fermi energy while it depends on the
cutoff energy, which is introduced to regularize the integration. We find that
the cutoff energy is appropriately determined by comparing the results for the
Wilson-Dirac lattice model, which approximates the massless Dirac Hamiltonian
around the Dirac point. We also calculate the spin susceptibility of massive
Dirac fermions for the model of topological insulators. We discuss the effect
of the band inversion and the strength of spin-orbit coupling.
