  Defect-induced magnetism in graphene has been predicted theoretically and
observed experimentally. However, there are open questions about the origin of
the magnetic behavior when substitutional impurities with $sp$ electrons are
considered. The aim of this work is to contribute to the understanding of
impurity-induced spin magnetism in doped graphene systems. Thus, the electronic
structure and spin magnetic moments for substitutional doped graphene with
impurities from groups IIIA (B, Al, and Ga) and VA (N, P, As, Sb, and Bi) of
the periodic table were obtained within the framework of density functional
theory. The nature of the magnetic ground state was determined from
calculations of the total energy as a function of the spin magnetic moment
using the fixed spin moment method. We show that the spontaneous magnetization
in the studied systems arises from an electronic instability by the presence of
a narrow impurity band at the Fermi level. Furthermore, we found that the
emergence of spin polarization requires the impurity to introduce an extra
electron to the graphene lattice and that the impurity-carbon hybridization is
close to the $sp^3$ geometry. These features reveal that the charge doping sign
and the hybridization degree play a fundamental role in the origin of $sp$
magnetism in substitutional doped graphene.
