In this work we consider an Abelian O(3) sigma model coupled nonminimally w
ith a gauge field governed by Maxwell and Chern-Simons terms. Bogomol'nyi e
quations are constructed for a specific form of the potential and generic n
onminimal coupling constant. Furthermore, topological and nontopological se
lf-dual soliton solutions are obtained for a critical value of the nonminim
al coupling constant. Some particular static vortex solutions (topological
and nontopological) satisfying the Bogomol'nyi bound are numerically solved
and presented. (C) 2000 Elsevier Science B.V. All rights reserved.