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We have studied the existence de self-dual solitons in a gauged version ofthe baby Skyrme model in which the gauge field dynamics is governed by theMaxwell-Chern-Simons action. For such a purpose, we have developed a detailedimplementation of the Bogomol'nyi-Prasad-Sommerfield formalism providing theself-dual equations whose solutions saturate the energy lower bound. Such abound related to the topological charge of the Skyrme field becomes quantizedwhereas both the total magnetic flux and the total electrical charge are not.We have found two types of self-dual Skyrme field profiles: the first isdescribed by a solution which decays following an exponential-law ($e^{-\alphar^2}$, $\alpha>0$); the second is portrayed by a solution having a power-lawdecay ($r^{-\beta}$, $\beta>0$). On other hand, in both cases the asymptoticbehavior of the gauge field is similar to the one presented in the context ofthe Abelian Higgs models describing Abrikosov-Nielsen-Olesen charged vortices.Other interesting feature we highlight is the localized magnetic fluxinversion, a property does not observed in others gauged baby Skyrme modelsalready studied in literature. Numerical results are presented for rotationallysymmetrical field configurations by remarking some of its essential features.

Self-dual solitons in a Maxwell-Chern-Simons baby Skyrme model