B^{3/2}$ and thus $\delta D\varepsilon\sim B^{1/2}$). Ignoring the Zeeman splitting, the valence and conduction band energy levels are equal with opposite sign, so their total contribution is canceled. Consequently, in order to study the magnetization in graphene at $\mu>0$ it is sufficient to work with equation (\[Mosc\]). It is worth noting that in this formalism, the spin splitting due to the Zeeman effect is already taken into account in equation (\[Mosc\]), so there is no need to introduce it as a reduction factor. The spin splitting is usually neglected in the MO calculations, but we will see that it can have a noticeable effect in $M$.

Spin splitting in the MO at zero temperature
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We shall now analyze equation (\[Mosc\]) in more detail. First, notice that each spin has a different amplitude $A_{s}$, although from equation (\[amp\]) we have $\left|A_{1}-A_{-1}\right|=\mu_{\mathrm{B}}B/\phi$, which usually is very small. On the other hand, the MO are periodic in $1/B$ (as in the classical case), each spin peak with the same frequency $\omega=\mu^{2}/\alpha^{2}$, but with a phase difference $2\Delta=4\mu_{\mathrm{B}}/\mu$. These features can be seen in figure \[fig1\], where the MO given by equation (\[Mosc\]) is plot for (a) low $\mu$ and (b) high $\mu$. 