  In honeycomb Dirac systems with broken inversion symmetry, orbital magnetic
moments coupled to the valley degree of freedom arise due to the topology of
the band structure, leading to valley-selective optical dichroism. On the other
hand, in Dirac systems with prominent spin-orbit coupling, similar orbital
magnetic moments emerge as well. These moments are coupled to spin, but
otherwise have the same functional form as the moments stemming from spatial
inversion breaking. After reviewing the basic properties of these moments,
which are relevant for a whole set of newly discovered materials, such as
silicene and germanene, we study the particular impact that these moments have
on graphene nanoengineered barriers with artificially enhanced spin-orbit
coupling. We examine transmission properties of such barriers in the presence
of a magnetic field. The orbital moments are found to manifest in transport
characteristics through spin-dependent transmission and conductance, making
them directly accessible in experiments. Moreover, the Zeeman-type effects
appear without explicitly incorporating the Zeeman term in the models, i.e., by
using minimal coupling and Peierls substitution in continuum and the
tight-binding methods, respectively. We find that a quasiclassical view is able
to explain all the observed phenomena.
