  The purpose of this paper is to study static solution configuration which
describes the magnetic monopoles in a scenary where the gravitation is coupled
with Higgs, Yang-Mills and fermions. We are looking for analysis of the energy
functional and Bogomol'nyi equations. The Einstein equations now take into
consideration the fermions' contribution for energy-momentum tensor. The
interesting aspect here is to verify that the fermion field gives a
contribution for non abelian magnetic field and for potential which minimise
the energy functional.
