The Klein paradox refers to counterintuitive reflection or transmission of relativistic particles from a potential barrier, which is a natural consequence of relativistic quantum theory. The realization of this paradox using fundamental particles is nearly impossible because of the high energy barrier that needs to be overcome. Graphene, with emergent gapless fermion excitations, allows for the study of the fermionic Klein paradox. The test of this paradox for bosonic particles, however, remains a challenging problem. Here, we show that the bosonic Klein paradox can be tested in a driven-dissipative magnonic system. By carefully designing the strength of external drivings through spin-orbit torque and internal dissipation of the magnet, both positive-energy states (magnon) and negative energy states (antimagnon) can be dynamically stabilized. The reflection of incident magnons at a barrier can be amplified to be larger than one, accompanied by a backflow antimagnon current. Our findings may benefit the amplification of magnons in spintronic devices and further enable magnonic system as a platform to study relativistic physics.
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