  Spin wave, the precession of magnetic order in magnetic materials, is a
collective excitation that carries spin angular momentum. Similar to the
acoustic or optical waves, the spin wave also possesses the polarization degree
of freedom. Although such polarization degrees of freedom are frozen in
ferromagnets, they are fully unlocked in antiferromagnets or ferrimagnets. Here
we introduce the concept of magnetic gating and demonstrate a spin wave analog
of the Datta-Das spin transistor in antiferromagnet. Utilizing the interplay
between polarized spin wave and the antiferromagnetic domain walls, we propose
a universal logic gate of pure magnetic nature, which realizes all Boolean
operations in one single magnetic structure. We further construct a full
functional 4-bit Arithmetic Logic Unit using only sixteen spin wave universal
logic gates, operating in a weaving fashion as a Jacquard loom machine. The
spin wave-based architecture proposed here also sets a model for the future
energy efficient non-volatile computing, the distributed processing-in-memory
computing, and the evolvable neuromorphic computing.
