  The effects of biaxial strain on the impurity-induced magnetism in P-doped
graphene (P-graphene) and N-doped silicene (N-silicene) are studied by means of
spin-polarized density functional calculations, using the supercell approach.
The calculations were performed for three different supercell sizes $4\times
4$, $5\times 5$, and $6\times 6$, in order to simulate three different dopant
concentrations 3.1, 2.0 and 1.4 %, respectively. For both systems, the
calculated magnetic moment is 1.0 $\mu_B$ per impurity atom for the three
studied concentrations. From the analysis of the electronic structure and the
total energy as a function of the magnetization, we show that a Stoner-type
model describing the electronic instability of the narrow impurity band
accounts for the origin of $sp$-magnetism in P-graphene and N-silicene. Under
biaxial strain the impurity band dispersion increases and the magnetic moment
gradually decreases, with the consequent collapse of the magnetization at
moderate strain values. Thus, we found that biaxial strain induces a magnetic
quantum phase transition in P-graphene and N-silicene.
