  The Stern-Gerlach (SG) effect is well known as the spin-dependent splitting
of a beam of atoms carrying magnetic moments by a magnetic-field gradient,
leading to the concept of electron spin. Antiferromagnets can accommodate two
magnon modes with opposite spin polarizations, which is equivalent to the spin
property of electrons. Here, we propose the existence of an all-magnonic SG
effect in antiferromagnetic magnonic system, where a linearly polarized
spin-wave beam is deflected by a straight Dzyaloshinskii-Moriya interaction
(DMI) interface into two opposite polarized spin-wave beams propagating in two
discrete directions. Moreover, we observe bi-focusing of antiferromagnetic spin
waves induced by a curved DMI interface, which can also spatially separate
thermal magnons with opposite polarizations. Our findings provide a unique
perspective to understand the rich phenomena associated with antiferromagnetic
magnon spin and would be helpful for polarization-dependent application of
antiferromagnetic spintronic devices.
