Einstein - de Haas Effect

This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod.

Is there a classical thought experiment in the vein of Veritasium or Steve Mould, that will help visualize the actual process?

So if I imagine being an iron atom sitting near the surface of the iron rod, what process ends up nudging me clockwise and anticlockwise around the rod's axis? Is it the applied field acting directly on my protons? Is it a tangential force acting on those of my electrons whose magnetic moments are contributing to the induced magnetization? If so, how does that force arise?

In this video [00:22] they use the gyroscope-and-swivel-chair experiment as an analogy to discuss the Einstein-de Haas effect.



Following the usual path, they just invoke conservation of angular momentum and call it a day.

But of course, if we wished, we could also drill down into the interactions that make up the process : the ends of the axle pulling and pushing on the professor's shoulders via his arms, which creates a torque about the stool's axis.

So in the actual E-d H experiment, what interactions (if any) transmit the forces / torque to the iron atoms?

I don't understand. In iron, the entire atom has a magnetic moment, and the electron is part of the atom. What needs to be transferred?

But if the spin magnetic moment is associated specifically with individual electrons, and some of those electrons flip their orientation, does it make no sense at all to inquire into what drives the atoms along circles around the z axis? Just as the bicycle wheel is what "owns" the initial "spin", and hence we can reasonably inquire into the forces transmitted along the professor's arms?

With the changing ## B ## there will necessarily be an ## E ## that gets created in a circular path in the x-y plane=the Faraday EMF=perhaps this is the additional piece you are looking for.

Wouldn't the Faraday EMF act equally on all the electrons and protons, and hence cancel out? It would cause some circulating eddy currents, though... but we can eliminate the distraction of eddy currents by considering a ferrite rod.

It's now a classical picture we are looking at, but the protons are bound and basically stationary, while the electrons orbit around the protons, and thereby the electric field can do more work on them. That picture is very classical, and not very precise, but it may again be part of what you are looking for.

and I don't know for sure whether it is the orbital part that causes the magnetic moment in iron or the spin part=something worth researching. and I think it is the spin part though, because I do remember something about the ## g_s \approx 2.0 ## in the de-Haas Einstein experiment. I think I may have that right, but it really needs to be researched to confirm.

Charles Link said:

It's now a classical picture we are looking at, but the protons are bound and basically stationary, while the electrons orbit around the protons, and thereby the electric field can do more work on them. That picture is very classical, and not very precise, but it may again be part of what you are looking for.

and I don't know for sure whether it is the orbital part that causes the magnetic moment in iron or the spin part=something worth researching. and I think it is the spin part though, because I do remember something about the ## g_s \approx 2.0 ## in the de-Haas Einstein experiment. I think I may have that right, but it really needs to be researched to confirm.

It definitely measures the spin gyromagnetic ratio. Einstein and de Haas measured something slightly larger than 1 and thought that was just experimental error (thinking it should be 1).

Swamp Thing said:

But if the spin magnetic moment is associated specifically with individual electrons

Nonsense. How do you point to an individual electron and say "that is the one where the magnet moment comes from". Just because they drew it that way on a random YouTube video doesn't mean that's what happens,

Agreed, to the extent that I should delete the word "individual" from the sentence you quoted.

But when you say ...

Vanadium 50 said:

In iron, the entire atom has a magnetic moment, and the electron is part of the atom.

... I'm not sure how that squares up with the idea that spin is a property of the electrons, and is "inherited" by the atom only because we choose to think of the atom as a single system. But if I understand correctly, the applied magnetic field is acting on one part of that system, i.e. the electrons, and causing them to flip.

Granted that we don't know which electrons among millions are going to flip (or have flipped already), we certainly do know that the magnetic field doesn't act directly on the nuclei or on the atom "as a whole". Or do we?

I do not think this helps. But if you are interested in the history of de Haas experiment, the experimental artifact was recently found in 2023, here is a piece from Ampère museum : https://www.univ-lyon1.fr/medias/fi...riment-epn-to-be-published-_1710166064460-pdf

Thanks, I will read the doc and get back if needed.

The most important thing here though I think is that the energy for the magnetic moment in the magnetic field is ## E=-\vec{\mu} \cdot \vec{B} ##. The magnetic moment will go to the other state for a spin ## 1/2 ## system as the magnetic field changes direction. There is also the exchange effect in the consideration of the energy, but those extra details they sometimes omit to keep things simple.

Edit: The exchange term will stay the same if all the spins are reversed.

An iron atom has 26 electrons. But you can't say "This electron is doing this, and this electron is doing that." You can say "Two electrons are in a 1S state", but you cannot say which two. In a real sense all of them are, and none of them are. You can only talk about the collection.

I need to research this further in that it may be worthwhile to find out if they used a permanent-magnet type iron or simply something whose magnetization is proportional to the applied field. I think I need to do some more reading and research on this or I may not have it at all correct. :)

The way I imagine this (quantum mechanically) is that as the magnetic field is applied the particles with magnetic moments plus spin precess but cannot change their (let's say z) component of angular momentum except by emitting/absorbing photons. These photons are then reabsorbed into the bulk motion of the material or some potentially radiating away. As the particles seek their lowest energy state there is a net transfer of angular momentum from the particle spins into the bulk motion of the material.

jambaugh said:

cannot change their (let's say z) component of angular momentum except by emitting/absorbing photons

I have been wondering if it could be phonons, hence my question in the quantum physics section..

I was also wondering if there is something like "torsional phonons" : google produces only about 200 results, so I'm not sure.

But your post leads to another tangential question, "if a circularly polarized laser falls on a highly absorbent medium, can we detect the torque with modern technology? Is this being done, say in academic lab experiments? Is it within reach of the home experimenter?"

For "phonons", I also wondered the same thing. I think that could be the case especially for nuclear spins, but nothing came up in a google. The reason may be that for nuclear spins, the substance would need to be cryogenically cooled for it to work.

Even with iron and electron spins, I anticipate it is probably an experiment that is somewhat difficult to perform, or university students would be seeing it as a laboratory exercise as part of their curriculum.

This document The microscopic Einstein-de Haas effect (Wells et al. 2019, J. Chem. Phys), somehow argues that spin-orbit coupling is necessary. As it is a macroscopic object, changes in spin have to be coupled to changes in the angular momentum of the lattice:

The EdH effect relies on the transfer of angular momentumfrom the electronic spins to the lattice of nuclei and thus highlights the role of spin-orbit coupling (SOC) in spin-lattice interactions.16 Without SOC, the direction of the electronic spin is decoupled from the orientation of the lattice and the EdH effect does notoccur.

It also argues that what is actually measured is the effective g-factor, that's why all the experiment I have found measure a number that is lower than 2 (for pure iron is between 1.8 and 1.9).

Charles Link said:

With the changing ## B ## there will necessarily be an ## E ## that gets created in a circular path in the x-y plane=the Faraday EMF=perhaps this is the additional piece you are looking for.

Wells et al (see pines-demon's post above) mention this as one contributing factor.

Another one from Wells et al, but involving ##\textup{Fe}_{15}## instead of ##\textup{O}_2## : https://arxiv.org/pdf/2308.03130.pdf