by equation (\[Mosc\]), for (a) low $\mu$ and (b) high $\mu$, where $\mu$ is the Fermi energy.](fig1.eps)

We can calculate the amplitude of the spin splitting effect in the MO by taking into account the low point of the first peak and the high point of the second peak, as schematically indicated in figure \[fig2\]. We consider the two peaks corresponding to a LL $l$, so that the first peak is located at $1/B_{1}=l/\omega-\Delta$, while the second peak at $1/B_{2}=l/\omega+\Delta$. Then, from equation (\[M0\]) we get that at the low point of the first peak we have $M_{1}=A_{1}/2-A_{-1}\arctan\left[\cot\left(2\pi\omega\Delta\right)\right]/\pi$, while at the high point of the second peak we have $M_{2}=A_{1}\arctan\left[\cot\left(2\pi\omega\Delta\right)\right]/\pi-A_{-1}/2$. Thus the amplitude of splitting $\Delta M_{S}$ is given by

![\[fig2\]Scheme of two peaks due to the Zeeman effect, located at $1/B_1=l/\omega-\Delta$ and $1/B_2=l/\omega+\Delta$. We define the amplitude of splitting $\Delta M_s$ as shown, which measures the observation of the Zeeman effect in the MO. Notice also that the peaks have a phase difference $2\Delta=4\mu_{\mathrm{B}}/\mu$.](fig2.eps)

![\[fig3\]Plot of the parameters $\Delta M_{s}/A_{+}$ and $2\Delta\omega$ as a function of the Fermi energy, where $\Delta M_{s}$ is given by equation (\[Delta Ms\]) and $A_{+}\equiv\left|A_{1}+A_{-1}\right|/2=\mu/\phi$. The phase $\Delta$ and frequency $\omega$ are given by 