Spin-orbit coupling

Happy new year! I want to write a little about what physicists call spin-orbit interactions. It turns out that there is a deep connection between electric and magnetic fields that can be made somewhat obvious by considering a thought experiment. (For a great discussion of this, see the textbook by Purcell.) Imagine a line of stationary positive charges. From our perspective (at rest relative to the line of charges), there is no current, so one should see an electric field pointed radially outward from the line of charges, and a positive charge placed next to the line of charges should respond accordingly, being pushed radially outward. Now consider viewing this from a reference frame moving parallel to the line of charges. From our point of view in that frame, we see a current, and therefore there should be a magnetic field associated with that current (as well as an electric field from the net positive charge). In special relativity, one can figure out how electric and magnetic fields transform into and out of each other when changing reference frames.

This shift of point of view is the way that spin-orbit coupling is usually explained in undergrad quantum mechanics. Consider a hydrogen atom. The electron zipping around the proton has a spin degree of freedom, and a corresponding magnetic moment. From the point of view of the (classically) moving electron, the proton is essentially a current producing a magnetic field, which will tend to align the electron magnetic moment. This couples the spin of the electron to the orbital motion of the electron; hence the name "spin-orbit coupling"; and it is technically a relativistic effect which tends to be bigger in heavier atoms.

Why should you care? Well, spin-orbit coupling can be important in solids, too, since one can think of their electronic states as being built out of atomic orbitals. As ZapperZ points out, a recent paper shows that these kinds of relativistic corrections are not necessarily tiny in ordinary, everyday solids.  In fact, it appears that it is essential to worry about such relativistic effects in order to understand why the electrochemical redox potentials of an ordinary car battery are what they are!