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

[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)?

 

[pines-demon]

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)?

View attachment 342197

Oh right! but I still do not get what is the solution hinted here. Isn't it just that we shouldn't think of the electron as a top perfectly pointing in the $x$ direction, but more like a precessing top with some projection in the $x$ direction (see image)?

 

[Swamp Thing]

This video goes into the details of what is going on when an electron in a lattice flips its spin direction under an external field. A key factor is the Gilbert damping, which is what eases the spin axis towards the final direction. If the electron were completely decoupled rotationally from the lattice, there would be no damping and it would precess for ever and not relax into the minimum energy direction. The direction of the damping torque is precisely what would transfer the (new - old ) angular momentum from electron to lattice and thus "balance the books".



But the following paper points out that the Gilbert damping term is a phenomenological element, and they

derive the Gilbert term from first-principles by a nonrelativistic expansion of the Dirac equation

.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.137601

Also, Charles Link's observation :

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.

... is confirmed by the authors when they say in their abstract,

this term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time-varying magnetic induction.

 

[Swamp Thing]

Dear moderators, maybe this thread could go into the Quantum Physics section?

 

[pines-demon]

@Swamp Thing could you please precise what are you still trying to understand here. Is there a question? or are we just commenting on the phenomena?

 

[Swamp Thing]

could you please precise what are you still trying to understand here.

As I said in my original question...

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?

... it seems to me that when one subsystem changes the direction of its angular momentum, and another subsystem then changes its own in order to preserve the total system angular momentum, then it implies that the second subsystem must experience a torque that drives it to change its angular momentum. And it also seems to me that sometimes it could be instructive to examine how that torque arises, and in this case I certainly felt curious to know more.

After finding the resources in my #37, my curiosity is satisfied: the transfer torque is down to the Gilbert damping, which in turn is derived in the paper linked to in my #37.