  Quantum information stored in local operators spreads over other degrees of
freedom of the system during time evolution, known as scrambling. This process
is conveniently characterized by the out-of-time-order commutators (OTOC),
whose time dependence reveals salient aspects of the system's dynamics. Here we
study the spatially local spin correlation function i.e., the expectation value
of spin commutator and the corresponding OTOC of Dirac--Weyl systems in one,
two, and three spatial dimensions. The OTOC can be written as the square of the
expectation value of the commutator and the variance of the commutator. In
principle, the problem features two energy scales, the chemical potential, and
the high energy cutoff. We find that only the latter is dominant, therefore the
time evolution is separated into only two different regions. The spin
correlation function grows linearly with time initially and decays as $t^{-2}$
for late times. The OTOC reveals a universal $t^2$ initial growth from both the
commutator and the variance while its late time decay, $t^{-2}$ originates from
the variance of the commutator. This late time decay is identified as a
characteristic signature or Dirac-Weyl fermions. These features remain present
also at finite temperatures. Our results indicate that Dirac--Weyl systems are
slow information scramblers and are essential when additional channels for
scrambling, i.e., interaction or disorder are analyzed.
