  We study the existence of BPS configurations in a restricted baby
Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic
permeability. In order to attain such a goal, we use the
Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the
lower bound for the energy and the BPS equations whose [electrically neutral]
solutions saturate that bound. During the energy minimization procedure, we
find a differential constraint which involves the self-dual potential, the
superpotential itself and also the magnetic permeability. In order to solve the
BPS system, we focus our attention on those solutions with rotational symmetry.
For that, we fix the magnetic permeability and select two BPS potentials which
exhibit a similar behavior near to the vacuum. We depict the resulting profiles
and proceed to an analytical description of the properties of the BPS magnetic
field. Furthermore, we consider some essential aspects of our model, such as
the conditions for the overall existence of the BPS solutions, and how the
permeability affects the magnetic flux. Finally, we present a family of exact
BPS solutions.
