In turn, when a gate voltage is applied, the electron density can be changed, which could be useful for spin filtering [@Hanson2004], spin-polarized currents in 2D systems [@Potok2003] and spin conductivity [@Sinitsyn2004]. Moreover, when other effects are considered, such as spin-orbit coupling due to an external electric field, the MO changes drastically [@Escudero2017a] and the interplay between the degeneracy of each level, the disorder and spin-orbit coupling is not trivial [@Escudero2017b].

Motivated by this, we analyzed the MO in pristine graphene, in the presence of a perpendicular magnetic field, taking into account the Zeeman effect. We have organized this work as follow: in section 2 we study the MO in graphene at zero temperature, taking into the account the Zeeman effect. We then analyze the conditions to observe the spin splitting in the MO. In section 3 we study the MO at nonzero temperature, where we make an approximation to obtain an useful analytical formula for the magnetization. From this we analyze how the temperature affects the observation of the spin splitting in the MO. We end with a study of the maxima and minima shift in the MO as a function of the temperature, from which we obtain an 