If electrons have no substructure and are considered point particles (according to the Standard Model), then how can they also have intrinsic spin? It would seem that the fact that they exhibit spin would indicate some further complexity to their structure, even if it may not be readily determined.
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First, the electron is not a point particle. The abstraction you are thinking of is what we would call a naked electron. In an experiment, you do not see the naked particle ever. It is always surrounded by virtual pairs. Hence, what you measure as the electron is really a many-body system.
Second, you might want to read this. The take-home message is "the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron". Another useful quote: "The spin is intrinsic, or inherent, i.e., it is a fixed feature of the wave field that does not depend on environmental circumstances. But it is not internal, i.e., it is not within the internal structure of the electron or photon".
Hector
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