  In this contribution, we start off from a fully relativistic description of a
single electron non-minimally coupled to an external electromagnetic field.
Making direct use of the field equation, instead of canonically deriving from
the Lagrangian density, the relativistic total angular momentum is attained,
where the effect of the relativistic torque due to the external sources is also
taken into account. Both the spin density and the orbital angular momentum
tensors are identified in the relativistic-covariant approach. Furthermore, the
symmetric and gauge invariant energy-momentum tensor is derived as well. In
addition, to inspect the non-relativistic regime, a perturbative expansion of
the field equation up to the leading order in $\left(v/c\right)$ is carried
out, where spin-orbit interaction terms naturally emerge in the
non-relativistic Hamiltonian as a consequence of the non-minimal coupling.
Features related to the spin currents, the spin-transfer torque and their
dependence on both magnetic and electric external fields are then calculated
and discussed. Considering that spin-orbit coupled systems are of particular
interest in the study of spin Hall effect, a two-dimensional (planar) scenario
of the system is contemplated, where the contributions to the Landau levels are
re-assessed. As a consequence of the planar regime and the non-minimal
coupling, a peculiar sort of fractionalization of the spin-up and -down
components emerges with the different spin components localized in distinct
positions.
