SmB$_6$ is a mixed valence compound and a well known candidate material for topological Kondo insulators. With the application of pressure the valence of Sm atoms increases and as a consequence antiferromagnetism emerges in experiments.
We have constructed a tight-binding model to describe the system after the spin exciton mode has condensed into one out of two possible antiferromagnetic orders: A-type and G-type. Interestingly, the magnetic orders lead to different topological properties. The A-type state exhibits nodal lines and gapped Dirac surface states, whereas the G-type state retains Dirac surface states, although time-reversal symmetry that protects them in the paramagnetic phase is broken. To distinguish the magnetic phases and to characterize the topological properties we study all band crossings, propose suitable crystalline topological invariants, and calculate the resulting surface states. Furthermore, we also consider the band topology in the high-field limit with a ferromagnetic order.