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

[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.