  In this work we analyze the effects of the application of an external
electric field in the formation of a local magnetic moment in silicene. By
adding an impurity in a top site in the host lattice and computing the real and
imaginary part of the self-energy of the impurity energy level, the polarized
density of states is used in order to obtain the occupation number of the up
and down spin formation in the impurity considering the mean field
approximation. Unequal occupation numbers is the precursor of a formation of a
local magnetic moment and this depends critically on the Hubbard parameter, the
on-site energy of the impurity, the spin-orbit interaction in silicene and the
electric field applied. In particular, it is shown that in the absence of
electric field, the boundary between the magnetic and non-magnetic phases
increases with the spin-orbit interaction with respect to graphene with a top
site impurity and shrinks and narrows it when the electric field is turned on.
The electric field effect is studied for negative and positive on-site impurity
energies generalizing the results obtained in the literature for graphene.
