  Antiferromagnetic topological insulators harbor topological in-gap surface
states protected by an anti-unitary $S$ symmetry, which is broken by the
inevitable presence of domain walls. Whether an antiferromagnetic topological
insulator with domain walls is gapless and metallic on its topological surfaces
remains to be elucidated. We show that a single non-statistical index
characterizing the magnetic order of domain wall-decorated antiferromagnetic
topological insulator, referred to as the Ising moment, determines the
topological surface gap, which can be zero even when the $S$ symmetry is
manifestly broken. In the thermodynamic limit, the topological surface states
tend to be gapless when magnetic fluctuation is bounded. In this case, the
Lyapunov exponent of the surface transfer matrix reveals a surface
delocalization transition near the zero energy due to a crossover from
orthogonal to chiral orthogonal symmetry class. Spectroscopic and transport
measurements on the surface states will reveal the critical behavior of the
transition, which in return bears on the nature of antiferromagnetic domains
walls.
