The Zeeman effect, showing the splitting of spectral emission lines
Only in external magnetic fields. And this effect can be also related to electron's own spin distributed statistically over cloud of definite shape.
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 magnetic. The spin-only formula is a good first approximation
for high-spin complexes of first-row transition metals.
Number of unpaired electrons Spin-only moment (μB)
1 1.73
2 2.83
3 3.87
4 4.90
5 5.92
The relationship is almost linear, although it is obvious that electrons occupy d-orbitals with different "magnetic numbers" M at the same L and N. The type of electron cloud does not affect magnetic phenomena, at least at relatively large distances from the atom. It seems that the images of electrons spinning around a nucleus in books for schoolchildren and students are fiction and are of purely historical interest. Except for "Rydberg atoms," where an entire electron cloud can make coordinated movements. Which is not surprising, since the solutions of the Schrödinger or Pauli equations give the probabilities of finding an electron, respectively, the distribution of charge density and proper magnetic moment (spin), but do not indicate the prevailing direction of velocity at that point. Consequently, the movements are either completely chaotic, with equal probability in either direction, or mutually compensated so that no resulting magnetic moment is formed. For example, if the prevailing direction of velocity coincides with the gradient of the wave function or its square, and since the vector potential would be directed so, and the magnetic field represents its curl, and the curl of any gradient is zero.