Evidence for half-integer ``angular momentum''

If a beam of neutral, paramagnetic atoms, such as silver atoms, is shot through a magnetic field, the beam can be split into two beams by the field as shown below:

図 1:

This is known as a Stern-Gerlach experiment. The fact that the magnetic field can split the beam into two suggests that there must be some intrinsic property that couples to the magnetic field like an angular momentum but that can take on half-integer values. This cannot be an orbital angular momentum, since $l$ can only take on integral values.