  In a collinear antiferromagnet with easy-axis anisotropy, symmetry dictates
that the spin wave modes must be doubly degenerate. Theses two modes,
distinguished by their opposite polarization and available only in
antiferromagnets, give rise to a novel degree of freedom to encode and process
information. We show that the spin wave polarization can be manipulated by an
electric field induced Dzyaloshinskii-Moriya interaction and magnetic
anisotropy. We propose a prototype spin wave field-effect transistor which
realizes a gate-tunable magnonic analog of the Faraday effect, and demonstrate
its application in THz signal modulation. Our findings open up the exciting
possibility of digital data processing utilizing antiferromagnetic spin waves
and enable the direct projection of optical computing concepts onto the
mesoscopic scale.
