magnetic moment

A magnetic moment is the measure of how strongly something behaves as a little magnet, with a north and a south pole. A charged particle that carries angular momentum, whether from orbiting or from spin, also carries a magnetic moment, because moving charge is what makes magnetism. So a spinning charged particle acts like a tiny bar magnet, and that is precisely what lets a magnetic field push it around.

Because spin is quantized, so is the magnetic moment that comes with it. For an electron the moment can line up only two ways with respect to an applied field, with energies slightly above or below the field-free value. This tiny energy split is what a Stern–Gerlach magnet exploits to fan a beam into separate spots, and it is the lever by which external fields couple to a particle's spin at all.

Spin magnetic moments add up to the magnetism you can feel. In iron and other ferromagnets vast numbers of electron spins line up, and their individual moments combine into the field of an ordinary magnet. The same coupling between spin moments and magnetic fields is what magnetic resonance imaging reads out to map the water in your body, turning a quantum property into a medical picture.