  We investigate the presence of topological structures and multiple phase
transitions in the O(3)-sigma model with the gauge field governed by Maxwell's
term and subject to a so-called Gausson's self-dual potential. To carry out
this study, it is numerically shown that this model supports topological
solutions in 3-dimensional spacetime. In fact, to obtain the topological
solutions, we assume a spherically symmetrical ansatz to find the solutions, as
well as some physical behaviors of the vortex, as energy and magnetic field. It
is presented a planar view of the magnetic field as an interesting
configuration of a ring-like profile. To calculate the differential
configurational complexity (DCC) of structures, the spatial energy density of
the vortex is used. In fact, the DCC is important because it provides us with
information about the possible phase transitions associated with the structures
located in the Maxwell-Gausson model in 3D. Finally, we note from the DCC
profile an infinite set of kink-like solutions associated with the parameter
that controls the vacuum expectation value.
