  The aim of this work is to describe the spin magnetization of graphene with
Rashba spinorbit coupling and Zeeman effect. It is shown that the magnetization
depends critically on the spin-orbit coupling l that is controlled with an
external electric field. In turn, by manipulating the density of charge
carriers, it is shown that spin up and down Landau levels mix introducing jumps
in the spin magnetization. Two magnetic oscillations phases are described that
can be tunable through the applied external fields. The maximum and minimum of
the oscillations can be alternated by taking into account how the energy levels
are filled when the Rashba-spin-orbit coupling is turned on. The results
obtained are of importance to design superlattices with variable spin-orbit
coupling with different configurations in which spin oscillations and spin
filters can be developed.
