  MnBi$_2$Te$_4$ (MBT) is a promising antiferromagnetic topological insulator
whose films provide access to novel and technologically important topological
phases, including quantum anomalous Hall states and axion insulators. MBT
device behavior is expected to be sensitive to the various collinear and
non-collinear magnetic phases that are accessible in applied magnetic fields.
Here, we use classical Monte Carlo simulations and electronic structure models
to calculate the ground state magnetic phase diagram as well as topological and
optical properties for few layer films with thicknesses up to six septuple
layers. Using magnetic interaction parameters appropriate for MBT, we find that
it is possible to prepare a variety of different magnetic stacking sequences,
some of which have sufficient symmetry to disallow non-reciprocal optical
response and Hall transport coefficients. Other stacking arrangements do yield
large Faraday and Kerr signals, even when the ground state Chern number
vanishes.
