# Einstein and de Haas

Q:
I am doing a research about the "Einstein and de Haas Experiment", but it is so difficult to find something useful about it. Could you explain the phenomenon that occurs? Thanks.
- Juliana
Brazil
A:
Here’s a quick explanation. Say that you’ve 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 it’s 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 there’s an external torque applied. Let’s 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. (I’m 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 wasn’t 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.

Mike W.

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 Faraday’s 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.

Tom

(published on 10/22/2007)

## Follow-Up #1: defects and Einstein-deHaas

Q:
How do you avoid effects due to non uniformity in the iron rod? If the rod were free of any permanent magnetic field of its own, presumably the ED effect would reverse if one reversed the applied field. However the above is hard to achieve.Since the ED effect is extremely small It appears to me that inhomogeneity would smother it.
- William simon (age 82)
rochester ny
A:
The inhomogeneities aren't particularly important. You thoroughly magnetize the iron first. It has the only magnetic field in the ED experiment. Certainly if one magnetized the iron the opposite direction, the resulting rotation upon demagnetization would reverse. That's not a bug but a feature- it helps to control for any little temperature-dependent torques in the string.

Mike W.

(published on 11/01/2011)

## Still Curious?

Expore Q&As in related categories