  We report on the development of the first integrated mid-infrared,
far-infrared and terahertz optical Hall effect instrument, covering an ultra
wide spectral range from 3 cm$^{-1}$ to 7000 cm$^{-1}$ (0.1-210 THz or 0.4-870
meV). The instrument comprises four sub-systems, where the
magneto-cryostat-transfer sub-system enables the usage of the magneto-cryostat
sub-system with the mid-infrared ellipsometer sub-system, and the
far-infrared/terahertz ellipsometer sub-system. Both ellipsometer sub-systems
can be used as variable angle-of-incidence spectroscopic ellipsometers in
reflection or transmission mode, and are equipped with multiple light sources
and detectors. The ellipsometer sub-systems are operated in
polarizer-sample-rotating-analyzer configuration granting access to the upper
left $3\times 3$ block of the normalized $4\times 4$ Mueller matrix. The closed
cycle magneto-cryostat sub-system provides sample temperatures between room
temperature and 1.4 K and magnetic fields up to 8 T, enabling the detection of
transverse and longitudinal magnetic field-induced birefringence. We discuss
theoretical background and practical realization of the integrated
mid-infrared, far-infrared and terahertz optical Hall effect instrument, as
well as acquisition of optical Hall effect data and the corresponding model
analysis procedures. Exemplarily, epitaxial graphene grown on 6H-SiC, a
tellurium doped bulk GaAs sample and an AlGaN/GaN high electron mobility
transistor structure are investigated. The selected experimental datasets
display the full spectral, magnetic field and temperature range of the
instrument and demonstrate data analysis strategies. Effects from free charge
carriers in two dimensional confinement and in a volume material, as well as
quantum mechanical effects (inter-Landau-level transitions) are observed and
discussed exemplarily.
