  In this work we address the ground state magnetization in graphene,
considering the Zeeman effect and taking into account the conduction electrons
in the long wavelength approximation. We obtain analytical expressions for the
magnetization at T=0 K, where the oscillations given by the de Haas van Alphen
(dHvA) effect are present. We find that the Zeeman effect modifies the
magnetization by introducing new peaks associated with the spin splitting of
the Landau levels. These peaks are very small for typical carrier densities in
graphene, but become more important for higher densities. The obtained results
provide insight of the way in which the Zeeman effect modifies the
magnetization, which can be useful to control and manipulate the spin degrees
of freedom.
