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I have read these questions:

Relation between magnetic moment and angular momentum -- classic theory

Why is the electron magnetic moment always parallel to the spin for an electron?

Does a magnetic field do work on an intrinsic magnetic dipole?

Isn't the spin only a synonym for the existence of a magnetic dipole moment and its direction?

Does a magnetic field arise from a moving charge or from its spin, or both?

Relationship Between Magnetic Dipole Moment and Spin Angular Momentum

where it says:

A spinning charged particle constitutes a magnetic dipole. Its magnetic dipole moment μ is proportional to its spin angular momentum S: μ=γS the proportionality constant γ is called the gyromagnetic ratio.

Is the magnetic field/force just a relativistic electric field/force or is there a fundamental difference?

where the comments say:

Because in a magnet, the atomic electrons are moving around their respective nuclei constituting a dipole and the dipoles are aligned in same direction to give net magnetic dipole moment.

So one is saying that magnetic dipole moment is caused by spin angular momentum, which is the intrinsic spin of an electron, the other one says that magnetic dipole is cause by electrons orbiting (orbital angular momentum) the nuclei (of course as per QM they are not classically orbiting).

So which one is right?

None of these questions says whether the magnetic dipole moment at QM level is caused by the intrinsic spin of electrons or the bound electrons' (OAM) orbiting (as per QM existing at a certain energy level) around the nuclei.

Question:

  1. Which one is right, is the magnetic dipole moment as per QM caused by the intrinsic spin of electrons or by electrons orbiting (OAM) the nuclei existing around the nuclei at a certain energy level?
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  • $\begingroup$ Árpád, noting prvents us from declairing the magnetic dipole of the electron as same fundamental as the electric charge. They both are intrinsic - independend from outer circumstances - properties. The spin, which always is parallel (or ant-parallel) to th moment, occurs in two situations. 1. as the deflection of moving electrons in external magnetic fields. 2. as the orientation in atoms and in molecules. Applying to the spin a revolving of the electron has historical roots but has to be obsolet today. $\endgroup$
    – HolgerFiedler
    Commented Jul 12, 2018 at 5:40
  • $\begingroup$ To add a little bit more pepper: I think the magnetic diople is more fundamental as the elctric charge. You could interprete the interaction inside atoms between protons and electrons as a lost of charge strength. More here $\endgroup$
    – HolgerFiedler
    Commented Jul 12, 2018 at 5:41
  • $\begingroup$ Thank you. Can you please tell me more about this: "The spin, which always is parallel (or ant-parallel) to th moment, occurs in two situations. 1. as the deflection of moving electrons in external magnetic fields. 2. as the orientation in atoms and in molecules." How does deflection make dipole moment, and how does orientation of atoms make dipole moment? $\endgroup$
    – Árpád Szendrei
    Commented Jul 12, 2018 at 5:55
  • $\begingroup$ I’m busy at the moment. Read the links in the link above. $\endgroup$
    – HolgerFiedler
    Commented Jul 12, 2018 at 6:12
  • $\begingroup$ @ÁrpádSzendrei Please bear in mind that Holger's assertion that the spin "has to be obsolete today" is basically just wrong, and s/he has been banging on the drum that "the magnetic dipole is more fundamental [than] the electric charge" for years despite a total lack of evidence to support that (and explicit answers to the contrary when s/he actually asked about it). Please do not fall for this sustained attempt at using this site as a soapbox to spread misinformation. $\endgroup$
    – Emilio Pisanty
    Commented Jul 12, 2018 at 11:01

2 Answers 2

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Spin and orbital angular momentum are two independent contributions to the total angular momentum. The ratio between angular moment and magnetic moment is called the g-factor. For the magnetic moment operator one has $\vec M /\mu_B = g_L \vec L + g_S \vec S$. The electron spin contributes with g=2 and orbital moment with g=1. The expectation value of this operator gives the magnetic moment. $\mu_B$ is the Bohr magneton.

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  • $\begingroup$ So magnetic dipole moment is caused by intrinsic spin? And it is not caused by bound electrons around the nuclei? $\endgroup$
    – Árpád Szendrei
    Commented Jul 12, 2018 at 0:06
  • $\begingroup$ I interpreted your question as being about electron dipole moment. I have adapted the answer to the general case. $\endgroup$
    – my2cts
    Commented Jul 12, 2018 at 6:40
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All that somehow relates to spin in QM becomes pretty complicated if you want to understand it fully and formally. Spin doesn't make ANY sense as a intristic moment of particles, when it comes to hard cases, as explaining why photons for example have spin = 1. The true logic and meaning behind spin is transformation of your particle wave-function upon rotations. Orbital contribution to magnetic dipole moment is intuitive from classical physics and it's pretty ok to think about it as it is. To derive spin part of magnetic dipole, we must go much deeper, to the Dirac equation for particles of spin 1/2. In QM, every thing makes sense only if it is in hamiltonian (and actually in field theory, from which magnetic dipole arises, it too just pop's out of energy multipole series). Using non-relativistic first order correction to hamiltonian from dirac equation, you get an additional term in hamiltonian, which is precisely spin * bor_magneton * magnetic field. It's not easy, but it is the only true way to obtain why spin contributes to magnetic dipole. Dirac got nobel prise for this.

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