The Einstein-de Haas effect

Angular momentum in classical physics is a well-defined quantity tied to the motion of mass about some axis - its value (magnitude and direction) is tied to a particular choice of coordinates.  When we think about some extended object spinning around an axis with some angular velocity \(\mathbf{\omega}\), we can define the angular momentum associated with that rotation by \(\mathbf{I}\cdot \mathbf{\omega}\), where \(\mathbf{I}\) is the "inertia tensor" that keeps track of how mass is distributed in space around the axis.  In general, conservation of angular momentum in isolated systems is a consequence of the rotational symmetry of the laws of physics (Noether's theorem). 

The idea of quantum particles possessing some kind of intrinsic angular momentum is a pretty weird one, but it turns out to be necessary to understand a huge amount of physics.  That intrinsic angular momentum is called "spin", but it's *not* correct to think of it as resulting from the particle being an extended physical object actually spinning.  As I learned from reading The Story of Spin (cool book by Tomonaga, though I found it a bit impenetrable toward the end - more on that below), Kronig first suggested that electrons might have intrinsic angular momentum and used the intuitive idea of spinning to describe it; Pauli pushed back very hard on Kronig about the idea that there could be some physical rotational motion involved - the intrinsic angular momentum is some constant on the order of \(\hbar\).  If it were the usual mechanical motion, dimensionally this would have to go something like \(m r v\), where \(m\) is the mass, \(r\) is the size of the particle, and \(v\) is a speed; as \(r\) gets small, like even approaching a scale we know to be much larger than any intrinsic size of the electron, \(v\) would exceed \(c\), the speed of light.  Pauli pounded on Kronig hard enough that Kronig didn't publish his ideas, and two years later Goudsmit and Uhlenbeck established intrinsic angular momentum, calling it "spin".

Because of its weird intrinsic nature, when we teach undergrads about spin, we often don't emphasize that it is just as much angular momentum as the classical mechanical kind.  If you somehow do something to a system a bunch of spins, that can have mechanical consequences.  I've written about one example before, a thought experiment described by Feynman and approximately implemented in micromechanical devices.  A related concept is the Einstein-de Haas effect, where flipping spins again exerts some kind of mechanical torque.  A new preprint on the arxiv shows a cool implementation of this, using ultrafast laser pulses to demagnetize a ferromagnetic material.  The sudden change of the spin angular momentum of the electrons results, through coupling to the atoms, in the launching of a mechanical shear wave as the angular momentum is dumped into the lattice.   The wave is then detected by time-resolved x-ray measurements.  Pretty cool!

(The part of Tomonaga's book that was hard for me to appreciate deals with the spin-statistics theorem, the quantum field theory statement that fermions have spins that are half-integer multiples of \(\hbar\) while bosons have spins that are integer multiples.  There is a claim that even Feynman could not come up with a good undergrad-level explanation of the argument.  Have any of my readers every come across a clear, accessible hand-wave proof of the spin-statistics theorem?)