What Determines the Precession Angle of an Electron in a Magnetic Field?

[drodophila]

Hi again,

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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[azntoon]

Yes, this assumption is realistic. The angle between the spin magnetic moment and the external magnetic field can vary depending on the interactions between the electrons in the material and their local environment. The effects of lattice distortions or spin-orbit coupling can cause the total spin magnetic moment vector to be inclined away from the external magnetic field, leading to a different spin value than one expected from a purely classical picture. Additionally, correlations between electrons in the material can also lead to a different spin value than what is expected from a classical picture.

 

[denian]

I would like to provide a response to your question about the electron precession angle and the dependence of this angle on the spin magnetic moment and magnetic field.

Firstly, it is important to note that the precession angle of an electron under a magnetic field is not a fixed value, but rather it changes depending on the direction and strength of the magnetic field. This is due to the fact that the Larmor frequency, which determines the precession frequency, is directly proportional to the strength of the magnetic field. So, as the magnetic field changes, the precession angle will also change.

Additionally, the angle between the spin magnetic moment and the magnetic field is not a fixed value either. It can change depending on the orientation of the electron's spin and its interaction with the magnetic field. In some cases, the angle may be 54.73 degrees as you mentioned, but it can also vary depending on the specific system being studied.

In terms of the dependence of this angle, it can be influenced by various factors such as the strength and direction of the magnetic field, the spin value of the electron, and any interactions with other particles or the lattice structure of the material. There is no specific law that determines this angle, as it is a complex phenomenon that is influenced by multiple variables.

In regards to your assumption about the classical picture explaining the difference in spin values in many-electron systems, it is important to note that classical physics cannot fully explain the behavior of electrons in such systems. The quantum nature of electrons and their interactions with other particles and the lattice must be taken into account in order to fully understand their behavior.

Overall, the electron precession angle and its dependence on various factors is a complex topic that requires further research and study to fully understand. I hope this response has provided some insight into the topic and I encourage you to continue exploring it further.