What Causes the Einstein - de Haas Effect in Iron Rods?

[Swamp Thing]

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?

 

[Swamp Thing]

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?

 

[Vanadium 50]

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?

 

[Swamp Thing]

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?

 

[Charles Link]

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.

 

[Swamp Thing]

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.

 

[Charles Link]

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.

 

[pines-demon]

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).

 

[Vanadium 50]

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,

 

[Swamp Thing]

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

But when you say ...

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?

 

[pines-demon]

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

 

[Swamp Thing]

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

 

[Charles Link]

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.

 

[Vanadium 50]

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.

 

[Charles Link]

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. :)

 

[jambaugh]

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.

 

[Swamp Thing]

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?"

 

[Charles Link]

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.

 

[pines-demon]

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).

 

[Swamp Thing]

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.

 

[Swamp Thing]

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

 

[Charles Link]

It does appear this thing apparently is not completely simple. My experience with the de Haas- Einstein experiment comes from a textbook Modern Physics by Hugh D. Young. He makes it sound like spin one half electrons in the magnetic field that perhaps make a permanent magnet have their spins reversed as the magnetic field is changed in direction and that's all there is to it. In the last few years I have learned that it is very difficult to change the direction of the magnetization in a permanent magnet=it needs a very strong applied field in the other direction. and then there is the exchange effect connecting the spins. Glad to see you @Swamp Thing are looking into the de Haas-Einstein experiment in more detail. :)

 

[pines-demon]

A key ingredient, that I think might be missing in some discussions of the effect, seems to be that there was an alternating current applied to the solenoid (and not at DC current), and thus an AC magnetic field. The frequency is tuned to amplify the oscillations.

 

[Swamp Thing]

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.

Isn't it the case that "you can only talk about the collection" because the electrons are mutually indistinguishable? OTOH, since the electrons are distinguishable from the protons / nuclei and from the lattice generally, then it seems that the initial spin is unambiguously attached to the ensemble of electrons, and can only be exchanged with the lattice through some kind of interaction?

 

[pines-demon]

It does appear this thing apparently is not completely simple. My experience with the de Haas- Einstein experiment comes from a textbook Modern Physics by Hugh D. Young. He makes it sound like spin one half electrons in the magnetic field that perhaps make a permanent magnet have their spins reversed as the magnetic field is changed in direction and that's all there is to it. In the last few years I have learned that it is very difficult to change the direction of the magnetization in a permanent magnet=it needs a very strong applied field in the other direction. and then there is the exchange effect connecting the spins. Glad to see you @Swamp Thing are looking into the de Haas-Einstein experiment in more detail. :)

Does it matter if it is a permanent magnet? You could have a total magnetization always pointing up independently of the sign of the magnetic field and still make it work. I am kind of lost on how the microscopic theory explains this, however what is important is that some (at least an Avogadro number of) magnetic moments flip sign, and the change in angular momentum is related to this change.

 

[Vanadium 50]

only be exchanged with the lattice through some kind of interaction?

I don't understand. Is this not tautologically true? If one atom exchanges angularr momentum with another, how can we say it has not interacted?

The question seems to be very woolly. Are we talking about the Einstein-de Haas effect? Or are we talking about atomic magnetic moments? Or are we talking about ferromagnetism, which is a property of bulk iron more than iron atoms?

 

[Charles Link]

The change in angular momentum I think is very small, even if you get every electron to go to the other spin state. Let's try to quantify that: $mvr=\hbar \approx 1.0 E-34$ joule-sec. Let's work with 22 lbs. of iron=10 kg=10^4 grams. atom weight=56, so we have about 200 moles $\approx 1.2 E +26$ atoms, (I'm going to assume one electron per atom, even though there may be more than one), so that $mvr \approx 1.0 E-8$ joule-sec. The $10$ kg of iron has volume $\approx 1 E-3$ m^3, so that $r \approx .05$meters. Using $I \approx Mr^2/2 \approx .01$ gives $\dot{\theta}=\omega=mvr/I=1E-6$ radians/sec $\approx 5E-5$ degrees/sec. I didn't check the arithmetic carefully, but it appears (and I think this part is correct), any motion is extremely small and would be difficult to observe, even if you had one $\hbar$ for each electron.

 

[Swamp Thing]

Yes, they had to really struggle to get their final result, building three versions in the process. They used some high-Q torsional resonance to amplify the rotation -- using a glass wire to suspend the iron rod. And in the final version it was more of a needle rather than a rod -- 16 cm long and 1.7 mm in diameter. And an optical "pointer" to magnify the rotational oscillation.

Here is one of their papers:
https://dwc.knaw.nl/DL/publications/PU00012546.pdf

 

[pines-demon]

Yes, they had to really struggle to get their final result, building three versions in the process. They used some high-Q torsional resonance to amplify the rotation -- using a glass wire to suspend the iron rod. And in the final version it was more of a needle rather than a rod -- 16 cm long and 1.7 mm in diameter. And an optical "pointer" to magnify the rotational oscillation.

Here is one of their papers:
https://dwc.knaw.nl/DL/publications/PU00012546.pdf

Also again, if you have an AC field, and you tune to resonance, you can amplify the effect.

 

[pines-demon]

The question seems to be very woolly. Are we talking about atomic magnetic moments? Or are we talking about ferromagnetism, which is a property of bulk iron more than iron atoms?

A better question might be, are there any questions still? Or are we just commenting on the effect? I am on the latter path.

 

[pines-demon]

The change in angular momentum I think is very small, even if you get every electron to go to the other spin state. Let's try to quantify that: $mvr=\hbar \approx 1.0 E-34$ joule-sec. Let's work with 22 lbs. of iron=10 kg=10^4 grams. atom weight=56, so we have about 200 moles $\approx 1.2 E +26$ atoms, (I'm going to assume one electron per atom, even though there may be more than one), so that $mvr \approx 1.0 E-8$ joule-sec. The $10$ kg of iron has volume $\approx 1 E-3$ m^3, so that $r \approx .05$meters. Using $I \approx Mr^2/2 \approx .01$ gives $\dot{\theta}=\omega=mvr/I=1E-6$ radians/sec $\approx 5E-5$ degrees/sec. I didn't check the arithmetic carefully, but it appears (and I think this part is correct), any motion is extremely small and would be difficult to observe, even if you had one $\hbar$ for each electron.

According to the paper (link above), they had a 48,8 times amplification. Which lead to a $\omega\approx 6\times10^{-3}\,$rad/s (?) estimate. Maybe adjust for the parameters of the experiment, but you are in the ballpark.

 

[Charles Link]

According to the paper (link above), they had a 48,8 times amplification. Which lead to a ω≈6×10−3rad/s (?) estimate. Maybe adjust for the parameters of the experiment, but you are in the ballpark.

With the lighter mass, with less material, that would also make for a higher rate of rotation. :)

 

[Swamp Thing]

See slides 3 and 22 in this presentation:

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=32601

In slide 3 they ask the question: If a spin +X electron beam enters a Stern-Gerlach magnet and forks into two beams with spins +Z and -Z, what happened to the initial angular momentum?

On slide 22 they provide an answer:

Once the linear momentum for the two spin components is split, the transverse angular momentum is “released” to do work on the magnet system.

The quantum equivalent of a card trick. If a card “vanishes” magically from one deck,
it must reappear somewhere else. No mechanism for the transfer of angular momentum
need be invoked!

So according to them, it's a sort of "spooky action at a distance"?

===================
Edit: My classical lizard brain insists on "invoking a mechanism". So it's trying to argue that: The electron changing spin state is like a little armature producing a change in flux. This produces a back-EMF in the Stern-Gerlach magnet (if it's an electromagnet) or a tiny demagnetization (if it's a permanent magnet). In the latter case, an electron somewhere in the magnet should change spin. But OTOH, spooky action at a distance is a lot cooler, so there's that.

 

[pines-demon]

See slides 3 and 22 in this presentation:

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=32601

In slide 3 they ask the question: If a spin +X electron beam enters a Stern-Gerlach magnet and forks into two beams with spins +Z and -Z, what happened to the initial angular momentum?

On slide 22 they provide an answer:


So according to them, it's a sort of "spooky action at a distance"?

===================
Edit: My classical lizard brain insists on "invoking a mechanism". So it's trying to argue that: The electron changing spin state is like a little armature producing a change in flux. This produces a back-EMF in the Stern-Gerlach magnet (if it's an electromagnet) or a tiny demagnetization (if it's a permanent magnet). In the latter case, an electron somewhere in the magnet should change spin. But OTOH, spooky action at a distance is a lot cooler, so there's that.

Maybe I am missing the trick here, but doesn't the magnetic field exert a torque? (so no conservation of angular momentum). Anyway I think this is enoughly different from the Einstein–De Haas experiment so maybe make another thread for this?

 

[Swamp Thing]

Maybe I am missing the trick here, but doesn't the magnetic field exert a torque? (so no conservation of angular momentum). Anyway I think this is enoughly different from the Einstein–De Haas experiment so maybe make another thread for this?

The magnetic torque on the input electron's dipole would be around the axis of propagation (y in the figure), no? Whereas the input spin that "disappears" during the transit is directed away from the page (X)?