Fermion exchange interaction between magnetic Skyrmions

Abstract

We propose a new mechanism of exchange interaction between the solitons related with the presence of localized fermions. Since the Atiyah-Patodi-Singer index theorem implies that such modes always exist for any topological soliton, their appearance may significantly alter the usual pattern of interaction. We elaborate this possibility considering, as a particular example, the chiral magnetic skyrmions coupled to spin-isospin fermions. It is shown that there are sequences of fermionic modes localized on the skyrmions. We investigate the additional effect of exchange interaction between the soltions with localized fermionic modes and demonstrate the existence of a stable system of magnetic skyrmions bounded by the strong attractive interaction mediated by the chargeless fermions.