  We theoretically study the scattering of spin waves from a sharp domain wall
in an antiferromagnetic spin chain. While the continuum model for an
antiferromagnetic material yields the well-known result that spin waves can
pass through a wide domain wall with no reflection, here we show that, based on
the discrete spin Hamiltonian, spin waves are generally reflected by a domain
wall with a reflection coefficient that increases as the domain-wall width
decreases. Remarkably, we find that, in the interesting case of an atomically
sharp domain wall, the reflection of spin waves exhibits strong dependence on
the state of circular polarization of the spin waves, leading to mainly
reflection for one polarization while permitting partial transmission for the
other, thus realizing an atomic-scale spin-wave polarizer. The polarization of
the transmitted spin wave depends on the orientation of the spin in the sharp
domain wall, which can be controlled by an external field or spin torque. Our
utilization of a sharp antiferromagnetic domain wall as an atomic-scale
spin-wave polarizer leads us to envision that ultra-small magnetic solitons
such as domain walls and skyrmions may enable realizations of atomic-scale
spin-wave scatterers with useful functionalities.
