  Mechanical modulation of the lattice parameter can modify the electronic
structure and manipulate the magnetic coupling of a material without
introducing impurities. Inspired by success in pressure-controlled magnetism,
we investigate the effect of hydrostatic pressure on quantized Chern states in
the antiferromagnetic topological insulator MnBi2Te4, using transport as a
probe. We show that pressure can enhance the robustness of quantum anomalous
Hall (QAH) phases that are otherwise delicate in 7SL MnBi2Te4 and in the
spin-flop (SF) state of 8SL MnBi2Te4. We explain our findings using a coupled
Dirac cone model of MnBi2Te4, which identifies stronger hybridization between
van der Waals layers as the driver of topological states. We further
demonstrate that moderate pressures readily available in laboratory systems can
provide reversible control of magnetic and topological phases. Our results
reveal a strong connection between the mechanical engineering of band topology
and magnetism.
