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

Effective field theory of low-energy excitations (magnons) that describe antiferromagnets is mapped into electrodynamics of a charged scalar field interacting with an external magnetic background. In this theory magnons and antimagnons are described by a corresponding scalar field. If the external background is a constant inhomogeneous magnetic field in the quantum version of the model, then there exists vacuum instability which can be analyzed by an analogy with the scalar QED with electric potential steps. Here magnons and antimagnons are treated as charged particles, whereas the magnetic moment plays the role of the electric charge such that magnons and antimagnons differ from each other in the sign of this moment. The vacuum instability is related to the magnon-antimagnon production from the corresponding vacuum by magnetic field inhomogeneities. Characteristics of the vacuum instability can be calculated nonperturbatively using special exact solutions of the Klein-Gordon equation. In particular, we consider examples of the magnetic field that correspond to some regularizations of the Klein step. In the case of smooth-gradient steps, we have derived a universal behavior of the flux density of created magnon-antimagnon pairs. It is noted that there exists an opportunity, for the first time, to observe the Schwinger effect in the case of Bose particle creation. Moreover, it turns out that in the case of the Bose statistics appears a new mechanism for amplifying the effect of pair creation, which we call statistically assisted Schwinger effect.