The Stern-Gerlach experiment
The „Directional quantization“ of Spins was shown in an experiment by Otto Stern and Walther Gerlach in 1922 (see figure): In a special magnetic field magnetic particles are deflected further upwards, the further their north pole points upwards, and further downwards, the further down their north pole points. If the poles are aligned horizontally, no deflection takes place. According to classical physics, we would expect that particles moving through the apparatus would have their north pole pointing randomly in all possible directions, and correspondingly all possible deflections could be observed. However, in an experiment with silver atoms, Stern and Gerlach were able to prove that there are only exactly two small dots on the screen.
Thus, they were able to demonstrate the "directional quantization" of the spin of the particles: The spin of silver atoms, like that of electrons, can only have exactly two orientations in a magnetic field. As a result, half of the particles are deflected upwards, the other half equally far downwards, and two dots appear on the screen.