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Effective field theory of low-energy exitations-magnons that describesantiferromagnets is mapped into scalar electrodynamics of a charged scalarfield interacting with an external electromagnetic potential. In the presenceof a constant inhomogeneous external magnetic field the latter problem istechnically reduced to the problem of charged-particle creation from the vacuumby an electric potential step (x-step). Magnetic moment plays here the role ofthe electric charge, and magnons and antimagnons differ from each other in thesign of the magnetic moment. In the framework of such a consideration, it isimportant to take into account the vacuum instability (the Schwinger effect)under the magnon-antimagnon production on magnetic field inhomogeneities (ananalog of pair creation from the vacuum by electric-like fields). Wedemonstrate how to use the strong field QED with x-steps developed by theauthors (SPG and DMG) to study the magnon-antimagnon pair production onmagnetic field inhomogeneities. Characteristics of the vacuum instabilityobtained for some magnetic steps that allows exact solving the Klein-Gordonequation are presented. In particular, we consider examples of magnetic stepswith very sharp field derivatives that correspond to a regularization of theKlein step. In the case of smooth-gradient steps, we describe an universalbehavior of the flux density of created magnon pairs. We also note that sincethe low-energy magnons are bosons with small effective mass, then for the firsttime maybe the opportunity will arise to observe the Schwinger effect in thecase of the Bose statistics, in particular, the bosonic Klein effect inlaboratory conditions. Moreover, it turns out that in the case of the Bosestatistics appears a new mechanism for amplifying the effect of the paircreation, which we call statistically-assisted Schwinger effect.

Schwinger mechanism of magnon-antimagnon pair production on magnetic field inhomogeneities and the bosonic Klein effect