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

Abstract

Effective field theory of low-energy exitations-magnons that describes antiferromagnets is mapped into scalar electrodynamics of a charged scalar field interacting with an external electromagnetic potential. In the presence of a constant inhomogeneous external magnetic field the latter problem is technically reduced to the problem of charged-particle creation from the vacuum by an electric potential step (x step). Magnetic moment plays here the role of the electric charge, and magnons and antimagnons differ from each other in the sign of the magnetic moment. In the framework of such a consideration, it is important to take into account the vacuum instability (the Schwinger effect) under the magnon-antimagnon production on magnetic field inhomogeneities (an analog of pair creation from the vacuum by electric-like fields). We demonstrate how to use the strong field QED with x steps developed by the authors (SPG and DMG) to study the magnon-antimagnon pair production on magnetic field inhomogeneities. Characteristics of the vacuum instability obtained for some magnetic steps that allows exact solving the Klein-Gordon equation are presented. In particular, we consider examples of magnetic steps with very sharp field derivatives that correspond to a regularization of the Klein step. In the case of smooth-gradient steps, we describe an universal behavior of the flux density of created magnon pairs. We also note that since the low-energy magnons are bosons with small effective mass, then for the first time maybe the opportunity will arise to observe the Schwinger effect in the case of the Bose statistics, in particular, the bosonic Klein effect in laboratory conditions. Moreover, it turns out that in the case of the Bose statistics appears a new mechanism for amplifying the effect of the pair creation, which we call statistically assisted Schwinger effect.