Spin Hall physics

As I mentioned during the APS meeting, Dan Ralph presented some beautiful work (for example) on spin torque devices (where the flow of spin-polarized electrons is able to rotate the magnetization of some "free" ferromagnetic layer of material).  This spin torque business is a fairly mature idea, and the early demonstrations of this effect made use of layered structures (ferromagnet/normal metal/ferromagnet), with the current flowing perpendicular to the layers.  That is, if electrons flow from FM1, some of them are spin-polarized because of the magnetization of FM1, and those polarized electrons traverse the normal layer into FM2.  That works fine, but the most angular momentum you're ever going to transfer that way is \( \hbar/2 \) per electron, and that assumes that the electrons from FM1 are perfectly polarized.   Suppose you could do better than this.  Is there some way, for a given amount of charge current that you flow, to get more angular momentum transferred?

The answer is "yes", and the key is to leverage the spin Hall effect.  (For a good summary of spin Hall physics, see this paper by one of the progenitors of the field - I'll briefly summarize.)  In the regular Hall effect, we think about charge current flow in a plane in the presence of a perpendicular magnetic field.  The charge carriers experience a Lorentz force from the magnetic field that pushes them in the plane transverse to the direction of the (longitudinal) charge current.  Net charge of one sign piles up at one transverse edge of the sample, and net charge of the other sign piles up at the opposite edge, until the force from the resulting transverse electric field balances the Lorentz force.  (Glad to see wikipedia has fixed the figure in this article.  A few years ago they had the direction of the Lorentz force backward.)  In the spin Hall effect, we again think about current flow in a plane.  However, there is no external magnetic field.  Instead, we have the current flowing in a material with strong spin-orbit scattering (that is, in the reference frame of the moving electron, the effective charge current due to the nuclei seemingly moving by produces enough of a magnetic field in that frame to couple significantly to the spin of the electron.  Fundamentally this is a relativistic effect!).  Because of the coupling of spin to orbital motion, if the charge carriers scatter, the spins self-polarize; spin-"up" electrons will pile up on one transverse edge of the sample, while spin-"down" electrons will tend to pile up on the opposite edge.  The extent to which this happens is determined mostly by the strength of the spin-orbit coupling, which is larger in heavier atoms.

So, Ralph and coworkers have used this effect to great advantage.  Instead of the FM/N/FM layered structure, they make a structure that looks like SO/FM/N/FM, where SO is a strong spin-orbit material, such as tungsten or platinum.  They can flow a current within the plane of the SO layer.  Through the spin Hall effect, this can pump polarized spins perpendicular to the plane, into the adjacent FM layer.  (The electrical resistance vertically through the FM/N/FM stack is a way of monitoring the relative alignment of the FM layers, thanks to the giant magnetoresistance.)  This is particularly clever, because for strong SO coupling in the SO layer, thanks to the large contact area at the SO/FM interface, they can get more like 10 \( \hbar \) of angular momentum per electron flowing within the SO layer.   Fascinating to realize that these effects (because they originate from SO physics) are really dramatic experimental proof of the way electric and magnetic fields obey special relativity!