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It is well known the precession frequency of a free electron under a magnetic field, know as the Larmor frequency. However, i have not found any mention to the angle between the spin magnetic moment and the magnetic field.

If the angle changes, to keep the same frequency the rotation linear speed will decrease or increase if the angle decreases or increases, respectively. v= angular speed x radius.

Is there any law that determines the dependence of this angle?

If we consider one single free electron, where Sz= S hbar and S=sqrt(S(S+1)), being S=1/2, then the angle is 54.73 deg.

However, in some materials, the spin value that gives a certain measured saturation magnetization (z-component of the spin magnetic moment) is not the same as the spin value necessary to obtain a given spin magnetic moment vector (the magnitude of the vector) that has been measured, for instance, by means of the Curie law for the same material.

Then, in many-electron systems where correlations and lattice effects may take place i think that a classical picture could explain the difference, i.e. the continuous inclination of the total spin vector may explain a Sz value not quantized.

Is this assumption realistic?

Here is the link where it is explained how we can obtain the total value of the spin magnetic moment by means of the Curie law:

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# Electron precession angle

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