Effect of an external electric field on local magnetic moments in silicene

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.