How quantum spin causes magnetism? I read about how spin and magnetism are related (mathematically) but I found that it is a concept related to classical physics which is in turn related to the idea of electrons actually spinning on their axis (which was later found impossible, at least as far as I know) but I wasn't able to find any relation between quantum spin and magnetism.
Can you please help?
 A: Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum.
Particles with spin can possess a  magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by measuring the magnetic fields generated by the particles themselves.
The intrinsic magnetic moment $\mu$ of a spin $1/2$ particle with charge $q$, mass $m$, and spin angular momentum $\mathbf{S}$, is
$$\mu=\frac{g_sq}{2m}\mathbf{S}$$
where the dimensionless quantity $g_s$ is called the spin g-factor. For exclusively orbital rotations it would be $1$ (assuming that the mass and the charge occupy spheres of equal radius).
A: Since the electron has charge, its quantum spin creates intrinsically an Amperian current loop that gives rise to a magnetic moment. That is actually Ampère's law in Maxwell equations of Electromagnetism.
