  Magnetic monopoles have been realized as emergent quasiparticles in both
condensed matter and ultracold atomic platforms, with growing interests in the
coupling effects between the monopole and different magnetic quasiparticles. In
this work, interaction effects between monopoles and magnons are investigated
for an atomic pseudospin chain. We reveal that the monopole can excite a
virtual magnon cloud in the paramagnetic chain, thereby giving rise to a new
type of polaron, the monopole-cored polaron (McP). The McP is composed of the
monopole as the impurity core and the virtual magnon excitation as the dressing
cloud. The magnon dressing facilitates the Dirac string excitation and impacts
the monopole hopping. This induces an anti-trapping effect of the McP, which
refers to the fact that the dressing enhances the mobility of the McP, in
contrast to the self-trapping of the common polarons. Moreover, heterogeneous
bipolarons are shown to exist under the simultaneous doping of a north and a
south monopole. The heterogeneous bipolaron possesses an inner degree of
freedom composed of two identical impurities. Our investigation sheds light on
the understanding of how the coupling between the impurity core and the
dressing cloud can engineer the property of the polaron
