  Polarization, denoting the precession direction with respect to the
background magnetization, is an intrinsic degree of freedom of spin wave. Using
magnetic textures to control the spin wave polarization is fundamental and
indispensable toward reprogrammable polarization-based magnonics. Here, we show
that due to the intrinsic cubic anisotropy, a $90^\circ$ antiferromagnetic
domain wall naturally acts as a spin wave retarder (wave-plate). Moreover, for
a $90^\circ$ domain wall pair developed by introducing a second domain in a
homogenous antiferromagnetic wire, the sign of retarding effect can be flipped
by simply switching the direction of the intermediate domain. The intimate
connection between rich states of magnetic domains and the spin wave
polarization in cubic anisotropic systems, offers new possibilities in
constructing purely magnetic logic devices.
