Robust A-type order and spin-flop transition on the surface of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$

Here we present microscopic evidence of the persistence of uniaxial A-type antiferromagnetic order to the surface layers of MnBi${}_2$Te${}_4$ single crystals using magnetic force microscopy. Our results reveal termination-dependent magnetic contrast across both surface step edges and domain walls, which can be screened by thin layers of soft magnetism. The robust surface A-type order is further corroborated by the observation of termination-dependent surface spin-flop transitions, which have been theoretically proposed decades ago. Our results not only provide key ingredients for understanding the electronic properties of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$, but also open a new paradigm for exploring intrinsic surface metamagnetic transitions in natural antiferromagnets.