Metamagnetism of few-layer topological antiferromagnets

${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT) materials are a promising class of antiferromagnetic topological insulators 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 noncollinear 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 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 nonreciprocal optical response and Hall transport coefficients. Other stacking arrangements do yield large Faraday and Kerr signals, even when the ground state Chern number vanishes.