  In Dirac materials, the low energy excitations obey the relativistic Dirac
equation. This dependence implies that the electrons are exposed to strong
spin-orbit coupling. Hence, real spin conservation is believed to be violated
in Dirac materials. We show that this point of view needs to be refined in the
semiclassical picture which applies to the case of doped Dirac materials (away
from the nodal point in the spectrum). We derive a novel type of Boltzmann
equation for these systems if they are brought slightly out-of-equilibrium.
Remarkably, spin-momentum locking is softened and a generalized spin
conservation law can be formulated. The most striking observable consequence of
our theory is a large transverse spin current in a nearly ballistic transport
regime.
