  We present a comprehensive study of the band structure of two- and
three-dimensional hexagonal layered materials using Landau Level optical Hall
effect spectroscopy investigations, employing graphene and graphite as model
systems. We study inter-Landau-level transitions in highly oriented pyrolytic
graphite and a stack of multilayer graphene on C-face 6\textit{H}-SiC, using
data from reflection-type optical Hall effect measurements in the mid-infrared
spectral range at sample temperatures of $T=1.5$~K and magnetic fields up to
$B=8$~T. We describe a comprehensive dielectric polarizability model for
inter-Landau-level transitions, which permits analysis of the optical Hall
effect data. From their magnetic field dependence we identify sets of H- and
K-point inter-Landau-level transitions in graphite and sets of
inter-Landau-level transition from decoupled graphene single, and coupled
graphene bi-, tri-, and quad-layer for the multilayer graphene stack. For
inter-Landau-level transitions in decoupled graphene single-layers and H-point
transitions in graphite we observe polarization mode preserving behavior,
requiring symmetric magneto-optical contributions to the corresponding
dielectric tensors. Inter-Landau-level transitions in coupled graphene layers
as well as K-point transitions in graphite exhibit polarization mode mixing
behavior, requiring antisymmetric magneto-optical contributions to the
corresponding dielectric tensors. From the circular-polarization-averaged
inter-Landau-level transition energies and the energy splitting between right-
and left-handed circular polarized inter-Landau-level transitions we determine
the model parameters in the Slonczewski-Weiss-McClure band structure
approximation for two- and three-dimensional hexagonal layered materials, with
graphene and graphite as examples.
