  Thin films of the topological insulator (BiSb)$_2$Te$_3$ oriented along the
[0001] direction were grown via molecular beam epitaxy on substrates of
Al$_2$O$_3$ (0001) and MgF$_2$ (110) single crystals, as well as on an
epitaxial thin film of the antiferromagnetic insulator MnF$_2$ (110).
Magnetoconductivity measurements of these samples showed close proximity of the
Fermi level to the Dirac point and weak antilocalization at low temperature
that was partially suppressed in the sample grown on the MnF$_2$ layer. The
magnetoconductivity data were fit to a model that describes the quantum
corrections to the conductivity for the Dirac surface state of a 3-dimensional
topological insulator, from which values of the Fermi velocity and the phase
coherence length of the surface state charge carriers were derived. The
magnetoconductivity of the (BiSb)$_2$Te$_3$ - MnF$_2$ bilayer samples were fit
to a model describing the crossover from weak antilocalization to weak
localization due to magnetic doping. The results are consistent with the
opening of an energy gap at the Dirac point in the (BiSb)$_2$Te$_3$ due to
magnetic proximity interactions of the topological surface states with the
antiferromagnetic MnF$_2$ insulator.
