From what I have read here, the concept of spin is attributed to a calculation based on a mathematical model using quantum mechanics. For example,
How can a particle with no size have angular momentum?
The experiment by Einstein and deHaas
https://www.dwc.knaw.nl/DL/publications/PU00012546.pdf
https://en.wikipedia.org/wiki/Einstein%E2%80%93de_Haas_effect
relied on the conservation of angular momentum. The simple youtube video
https://www.youtube.com/watch?v=4UK10VAVzXk
implies that you can get an iron cylinder dangling from a string to spin by imposing a magnetic field in the direction of the supporting string. The actual paper tho describes that a magnetic field has to be reversed ("Then, on reversing a current in K a rotation of C ought to be
observed.") This makes more sense as you first need to have all the angular momenta lined up. Then the reversal of the field induces angular momenta to 'flip'. I assume that the 'flipping' is caused by the Lorentz force of the new magnetic field on the intrinsic magnetic field of all the lined up atoms. I dont get why that should cause the cylinder to spin. For the Lorentz force to make the cylinder spin, the magnetic field of the coil should be transverse to the magnetic field of the cylinder.
However the authors then say " In reality, however, this simple method cannot be thought of. As the field of the coil will not be uniform the cylinder would probably show highly irregular motions completely masking the effect that is sought for. "
Obviously, they saw variations that obscured their data and 'non uniformity' is how they explained it. Personally, I cannot understand what 'non-uniformity' they are talking about.
They then go on to talk about using 'resonance', basically using an AC current to cause the field to oscillate and thence to cause the cylinder to spin back and forth.
The complexities introduced by pursuing the analysis of resonance are numerous, including the effect of the Earth's magnetic field.
Their use of mathematics borders on being a demonstration of their virtuoso skills. Perhaps I am too dense as I get lost in the weeds.
In addition remarks like "Unfortunately, when our experiments had been brought to a conclusion and one of us had left Berlin it came out that a mistake had been made in the application of the method, so that we must consider as a failure this part of our investigation." make me less confident about the whole experiment and its results.
Later experiments by Barnett
https://en.wikipedia.org/wiki/Barnett_effect
talk about the formation of a magnetic field simply by spinning a ferromagnetic material. I totally do not understand why that should happen if all the angular momenta in a lump of iron are randomly distributed. Anyway, I don't get how that tells you that electrons in an atom have angular momentum.
Further phenonmena such as electron spin resonance have been attributed to the intrinsic 'spin' of electrons.
https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#:~:text=Electron%20paramagnetic%20resonance%20(EPR)%20or,the%20spins%20of%20atomic%20nuclei.
Certainly, I understand that "increasing an external magnetic field, the gap between the
${\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}} m_\mathrm{s} = + \tfrac{1}{2} and {\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}} m_\mathrm{s} = - \tfrac{1}{2} $
energy states is widened until it matches the energy of the microwaves,..."
but how do you get from a widening energy gap to saying that it reflects 'spin'?
The wiki article says 'At this point the unpaired electrons can move between their two spin states. '
It's an energy gap, like the energy gap between orbitals of electrons in an atom. What is the evidence that tells us it is angular momentum and therefore prompts the confusing use of the word 'spin'.
I would appreciate referral to an honest, simple experiment that shows electrons in an atom have angular momentum.
