is sufficient to take only the $B_{n}$ between the range of magnetic fields considered.

In figure \[fig4\] it is show the magnetization given by equation (\[MT\]) for $\mu=250$ meV and temperatures (a) $T=0.1$ K, (b) $T=1$ K. We can see that as the temperature increases, the magnetization at $T\neq0$ broadens, similar to the Fermi-Dirac distribution with the DOS. Of course, this is exactly what is expected from the result given by equation (\[MT\]). Moreover, in figure \[fig4\](a) we see that at very low temperature $T=0.1$ K one can still appreciate the effect of the spin splitting in the magnetization, which results in a small bump around the two peaks. Nevertheless, as the temperature is increased, this bump disappears and the MO behave as maxima and minima around the center of the two peaks at zero temperature. Thus in this regime there would be no noticeable effect of the spin splitting in the magnetization. This is strongly dependent not only on the temperature, but also on the magnetic field and Fermi energy. In other words, for high magnetic fields, the temperature at which the spin splitting is negligible increases.

Spin splitting in the MO at nonzero temperature
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An estimation for 