The Stern-Gerlach measurement of silver atoms in 1922 first showed the unexpected up/down magnetism of neutral silver and other atoms that have a single, unpaired electron. The up/down magnetism of quantum electron spin is the basis of the quantum measurement problem in philosophy. Although the spin showed a 50:50 up:down magnetism, the measurement did not indicate that the original neutral atom was magnetized at all. In fact, the measurement itself seems to have affected the outcome of the neutral atom spin magnetism.
Although it was not clear why neutral atoms showed magnetism at all, just two years later in 1924 Pauli proposed that electrons with complementary spin can occupy the same space and time in a superposition. The math behind quantum spin became more apparent when Schrödinger discovered in 1926 the quantum mechanics equation that, for the first time, explained the spectrum of atomic hydrogen. It then became clear that the spin magnetism of electrons manifests itself in the fine structure of atomic hydrogen and spin magnetism of protons in the hyperfine structure of atomic hydrogen.
The notion of quantum spin was first thought to emerge from a rotating charged particle rotation like like an electron, since charged spheres were well know to induce classical magnetism. However, given the electron charge radius, the rotation velocity would be c/alpha, some 137 time the speed of light. Nevertheless, the notion of a spinning charge continues today as a simple explanation for quantum spin.
However, it is the fundamental quantum oscillation of matter that explains quantum spin. Quantum oscillation provides the electron oscillating electric field that then results in spin magnetism perpendicular to the electric field. Thus, instead of charge rotation, quantum spin is due to a perpetual oscillation of quantum wavefunctions that has no meaning for a classical particle of static mass and charge.
When the electron electric field oscillates in plane, there are two possible spin states as up for left or down for right as the figure shows. In addition to charge oscillation, electron mass also oscillates and so the electron mass amplitude oscillates much more slowly than electron charge amplitude as the figure shows.