Magnon Chirality Hall Effect in Antiferromagnet

In a collinear antiferromagnet with easy-axis anisotropy, symmetry dictates that the spin wave modes must be doubly degenerate with opposite chirality. We show that in the presence of the Dzyaloshinskii-Moriya interaction, there exist a magnon chirality Hall effect, where magnons with opposite chirality flow to opposite transverse edges when an in-plane temperature gradient is applied. Possible material candidates to realize this effect is also discussed.