We present theoretical evidence that atomically sharp domain walls in antiferromagnetic materials have qualitatively different properties from their smooth counterparts, in which the reversal of the antiferromagnetic order parameter occurs gradually over many unit cells. A remarkable difference appears when we consider the effect of the domain wall on the propagation of an antiferromagnetic spin wave. Antiferromagnetic spin waves, unlike ferromagnetic ones, have two possible states of circular polarization: left handed and right handed. While a smooth domain wall does not distinguish between the two cases, allowing both types of waves to be transmitted with high probability (tending to 100% in the infinitely smooth limit), an atomically sharp domain wall can act as a spin wave polarizer, i.e., it allows one type of polarization to be almost completely transmitted while the other is almost completely reflected. This remarkable behavior occur in the vicinity of a sharp to smooth transition, which is controlled, within our model, by the ratio of the easy axis anisotropy to the nearest-neighbor exchange constant. The polarization of the transmitted spin wave depends on the orientation of the spins in the sharp domain wall - a property which can be controlled by an external field or spin torque and has no counterpart in a smooth domain wall. Our discovery of the spin-wave polarizing properties of sharp antiferromagnetic domain walls suggests that they could be used as spin polarizers in magnonic circuits.
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