I Macroscopic rotation from spin flipping?

[Toothbrush]

There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.)

I could conceivably arrange this by passing all of my ring material through a Stern Gerlach experiment beforehand. If the alignment of the spins would decay too fast, I could get the same rotation by spraying spin-up silver on to a floating target, as it was coming from the magnets. The issue that I'm no so sure about is: how can I get the angular momentum to go into macroscopic motion, and not something else?

(I don't know enough physics to tell whether or not this boils down to designing the right lattice to spray the silver on to, so feel free to move my post.)

 

[berkeman]

Welcome to the PF.

There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.)

Could you post a reference link for that calculation please? Thanks.

 

[PeterDonis]

There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness

I don't know what you mean by "relaxing from spin-up into randomness".

assuming you could get all of it to show up externally

You can't. This would amount to converting an electron's intrinsic spin into orbital angular momentum, which can't be done for an electron since its spin is, well, intrinsic, and can't be converted to anything else.

 

[mfb]

You can't get rid of the electron spin, but flipping the spin of enough electrons can introduce a macroscopic rotation of the object. This is called Einstein-de Haas effect and has been verified experimentally. Typically both orbital angular momentum and spin contribute. For pure iron spin is dominant.

 

[PeterDonis]

flipping the spin of enough electrons can introduce a macroscopic rotation of the object

Just to be clear, this is inducing a macroscopic rotation by turning on a magnetic field. It is not the same as an object just sitting there "relaxing from spin up into randomness", as described in the OP.

 

[mfb]

Turning the magnetic field off and maybe heating the object (if ferromagnetic) could work as well.

 

[Toothbrush]

Could you post a reference link for that calculation please? Thanks.

I just did a little napkin calculation:

• delta angular momentum going from spin up to spin down = 1 hbar
• delta angular momentum from relaxation = 1 hbar * (number of electrons or silver atoms) / 2
  
• moment of inertia of 1cm radius ring = (number of atoms * mass per atom)*( 1cm^2 )
• Angular frequency = angular momentum / moment of inertia

The "number" factor cancels and we're left with a result that only depends on the mass of a silver atom (the mass per flipping electron), and the radius of the ring.

You can't get rid of the electron spin, but flipping the spin of enough electrons can introduce a macroscopic rotation of the object. This is called Einstein-de Haas effect and has been verified experimentally. Typically both orbital angular momentum and spin contribute. For pure iron spin is dominant.

That's great, exactly satisfies what I was wondering about.

 

[PeterDonis]

delta angular momentum from relaxation

This is the part I don't understand. If the system is not interacting with anything else, angular momentum is conserved, so there can't be any "delta angular momentum" just from "relaxation".

If the system is interacting with something else (as in the examples given by others), then the "delta angular momentum" comes from the interaction, not from "relaxation".

 

[Toothbrush]

... angular momentum is conserved...

Yes, the idea is that the decrease in the total spin angular momentum (m_j from all of the s-es) is balanced out by the object's macroscopic rotation. Like a reaction wheel on a satellite, except instead of reaction wheels you have lots of electrons that are having their spin projection quantum numbers changed.

 

[PeterDonis]

the idea is that the decrease in the total spin angular momentum (m_j from all of the s-es) is balanced out by the object's macroscopic rotation.

I meant "angular momentum is conserved in the absence of external interaction" in a more restrictive sense. All of the examples I am seeing here (including the Einstein-de Haas effect) involve the object interacting with an external field. In the absence of such an external field, I don't think you can "convert" electron spin angular momentum into macroscopic angular momentum of the object as a whole, which from the electron's standpoint would be orbital angular momentum.

In the case where the object is interacting with an external field, the angular momentum of the object by itself does not have to be conserved, since the field can also contain angular momentum and can exchange it with the object.

 

[Toothbrush]

I meant "angular momentum is conserved in the absence of external interaction" in a more restrictive sense. All of the examples I am seeing here (including the Einstein-de Haas effect) involve the object interacting with an external field. In the absence of such an external field, I don't think you can "convert" electron spin angular momentum into macroscopic angular momentum of the object as a whole, which from the electron's standpoint would be orbital angular momentum.

In the case where the object is interacting with an external field, the angular momentum of the object by itself does not have to be conserved, since the field can also contain angular momentum and can exchange it with the object.

There are fields internal to the object that can perturb the angular momenta. If this was not possible, magnetism would not experience thermal effects. See also: relaxation in NMR. Angular momentum can travel around in large thermal-energy-scale systems quite freely.

EDIT:
An external field would probably be necessary to prepare the initial conditions, but this problem deals with t>0.
The "turn off the field and warm the magnet" example involves no interaction with the outside world after the field is turned off, at which point the object wouldn't be moving yet. (Open question: what would you have to do to the electric field to stop the other terms from applying an unrelated torque? There's a curl in there somewhere...)

 

[PeterDonis]

There are fields internal to the object that can perturb the angular momenta.

Yes, that's true.

An external field would probably be necessary to prepare the initial conditions

Yes, I think that's correct.

 

[mfb]

In the case where the object is interacting with an external field, the angular momentum of the object by itself does not have to be conserved, since the field can also contain angular momentum and can exchange it with the object.

But it doesn't do that in the Einstein-de Haas effect.

Heating a magnetized ferromagnet above its Curie temperature should work as well.

 

[DrDu]

Just to be clear, this is inducing a macroscopic rotation by turning on a magnetic field. It is not the same as an object just sitting there "relaxing from spin up into randomness", as described in the OP.

I think it would happen if you heat a magnetised whisker rapidly above its Curie point.