Wherever the practical use of the magnetic moments of atoms is carried out, only the electrons own spins appear. For example, Wikipedia gives the following rule for calculating the moments of transition metals with a large number of unpaired electrons.
Many transition metal complexes are...
You are right. The topic initially was about experiments. I can hardly imagine what experiments can confirm the presence of magnetic moments in hydrogen-like ions. It is probably necessary to maintain a certain concentration of monatomic hydrogen or ionized helium with the help of radiation...
Fock's interpretation is the interpretation of quantum mechanics in terms of the concept of the reality of quantum states of a microobject. It was nominated by V. A. Fok and A. D. Alexandrov. He asserts that the wave function of each microobject is an objective characteristic of its real state...
It is problematic to acquaint you in more detail with the works of Fock, since they are written in Russian language. I will try to translate from here...
It seems to be a quite simple experiment, whether there is a difference between magnetic moments e.g. in the 2s and 2p states of an electron cloud of hydrogen or helium atom. But for some reason there is no such experimental data.
What is "quantum state" depends on interpretation of QM. There are 10 or more different interpretations. I prefer Hartree-Fock explanation of QM: statistical approach, separate wavefunction for each electron, physical reality of cloud and independence from observer.
I have no doubts that own magnetic moment of a single electron is equal to the Bohr's magneton. I suspect an electron in a "cloud" has no "orbital" motion, like planets are moving around the Sun. Motions are completely chaotic, with abrupt changes of direction and velocity. So, magnetic moment...
It is interesting information. Of course, cautious approach is required, because Rydberg states can be associated with whole electron cloud circular motion around a nucleus.
Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of...