  We use the first principles and effective Hamiltonian methods to study the
electronic structure and magnetic properties of a recently synthesized layered
antiferromagnetic square net topological semimetal EuZnSb$_2$ [1]. The main
message of the paper is that effects of small changes in the band structure
produced by the magnetic ordering and changes in the orientation of the \Neel
vector are amplified in such transport properties as the spin Hall
conductivity. We predict that the effects of the broken symmetry introduced by
the ordering of the \Neel vector, being very weak in the bulk, are pronounced
in the surface electronic dispersion, suggesting that surface probes may be
more suited to measure them. The coexistence of the magnetism with many other
competing phases make this material interesting and possibly useful for quantum
spintronics applications.
