Hereís a quick explanation. Say that youíve got a magnetized bar of iron dangling from a thread. The magnetism comes almost exclusively from the electrons. They can contribute in two ways to the magnetism. One is by actually making circulating currents, like the currents you create in an electromagnet. The other is that each electron already intrinsically acts like itís spinning around, so each is already magnetic. For each of these contributions, the magnetism is accompanied by some angular momentum, a measure of how much there is mass circulation around some axis.
Now angular momentum is conserved in a closed system. It only changes when thereís an external torque applied. Letís say that the magnet is gradually warmed up to its Curie temperature, at which it ceases to be magnetic. The magnetic moments of all the electrons, instead of lining up, get scrambled and point all directions. That means that the electrons are rotating counterclockwise as often as clockwise, so they have no net angular momentum.
Where does that angular momentum go? It goes into an overall rotation of the whole bar- something you can see and measure. So the experiment allows us to see how much electron angular momentum there is per each unit of magnetic moment. The magnetic moment per angular momentum ratio is called the gyromagnetic ratio. (Iím not sure if this was the precise method used initially, but it was something along those lines.)
The surprising thing about the Einstein-de Haas experiment results (as least when they were redone carefully by others- I think perhaps this wasnít noticed in the first round) is that the gyromagnetic ratio is about twice as big as you would calculate if you just assumed that the magnetism was from electrons making circulating currents, like in an electromagnet. It turns out that for the spin component of the magnetism, relativistic effects make the gyromagnetic ratio a little bigger than twice the obvious value. I would try to explain that if I understood it.
That gyromagnetic ratio has now become the most precisely known number in physics, measured to something like four parts per 100 billion. Furthermore, the value is correctly predicted to that accuracy by relativistic quantum electrodynamics.
You can actually extract some of this angular momentum in an interesting way by putting a ring of insulating material with charges stuck to it closely circling the magnetized iron rod. Heat the rod up and the total magnetic flux through the ring changes, and Faradayís law of induction says there must be a net electromotive force around the ring, pushing the ring around. The field of the charges on the ring acts back on the demagnetizing iron rod so that the total angular momentum is shared between the rod and the ring.
(published on 10/22/2007)