  Based on the theory of macroscopic quantum electrodynamics, we generalize the
expression of the Casimir force for nonreciprocal media. The essential
ingredient of this result is the Green's tensor between two nonreciprocal
semi-infinite slabs including a reflexion matrix with four coefficients that
mixes optical polarizations. This Green's tensor does not obey Lorentz's
reciprocity and thus violates time-reversal symmetry. The general result for
the Casimir force is analyzed in the retarded and nonretarded limits,
concentrating on the influences arising from reflections with or without change
of polarization. In a second step we apply our general result to a photonic
topological insulator whose nonreciprocity stems from an anisotropic
permittivity tensor, namely InSb. We show that there is a regime for the
distance between the slabs where the magnitude of the Casimir force is tunable
by an external magnetic field. Furthermore the strength of this tuning depends
on the orientation of the magnetic field with respect to the slab surfaces.
