  We theoretically investigate the features of Ruderman-Kittel-Kasuya-Yosida
(RKKY) exchange interaction between two magnetic impurities, mediated by the
interfacial bound states inside a domain wall (DW). The latter separates the
two regions with oppositely signed inversion symmetry broken terms in graphene
and Weyl semimetal. The DW is modelled by a smooth quantum well which hosts a
number of discrete bound states including a pair of gapless, metallic
zero-energy modes with opposite chiralities. We find clear signatures of these
interfacial chiral bound states in spin response (RKKY exchange interaction)
which is robust to the deformation of the quantum well.
