@Ardenghi2014; @Ardenghi2013; @Escudero2018]. Unlike conventional materials, the magnetization in graphene has unique features. This can be related to the Landau levels (LL) that appear when a magnetic field is applied [@Kuru2009]. In a classical system, these LL are equidistant due to the parabolic dispersion relation. But in graphene, at low energies the dispersion relation is relativistic [@Neto2009], causing the LL to be not equidistant, which in turn affects the oscillating behavior in the thermodynamics potentials [@Goerbig2011]. For instance, the magnetic oscillations (MO), the so called de Haas van Alphen effect [@deHaas], are sawtooth at zero temperature [@Sharapov2004; @Fu2011], with the peaks being caused by the change in the last occupied energy level [@Escudero2017].

The MO are altered by impurities and temperature. In each case the MO are broadened as a result of the modified density of states (DOS) and the Fermi-Dirac distribution. In classical metals this is described by the Lifshitz-Kosevich formula [@Shoenberg1984], which incorporates the effects of impurities and temperatures, as well as the spin. The essential feature of this formula is that the MO are written as an infinite series, where the damping effects are taken into account by the introduction of reduction factors. This formula has been 