How Do Electron Spins Influence Magnetism?

[channel1]

1 - How does an electron's spin generate its own magnetic field?
2 - Why are only the orientations of electrons taken into account in statements such as "permanent magnets are created when the orientations of the spin of the electrons are orientated in the same direction" when protons also have spin and generate their own magnetic moment as well...?

 

[Khashishi]

1. Classically, a moving charge generates a magnetic field. This is still true in quantum mechanics, but the formal math is very different, based on the Hamiltonian formulation. It comes in because the momentum is replaced by p-qA, where A is the vector potential. In the Dirac equation, eigenstates of the angular momentum will work out to have different energies within a magnetic field. We interpret this as the electron having its own magnetic field, interacting with the external field.

2. The electron magnetic moments are much larger than the nuclear magnetic moments, so the nuclear magnetic moments can be neglected. This would be expected if the electron and nucleus behaved classically: the nucleus is much more massive so it turns much more slowly for an equivalent angular momentum, so it produces much less magnetic field. Obviously, you can't rely on classical mechanics here, but classical mechanics can still give some useful insights I think.