In its rest frame, an electron orbiting a nucleus feels a magnetic field proportional to its speed. The faster the electron orbits, the stronger the magnetic field, and the greater the coupling between the electron’s spin and orbital momenta.

Spin–orbit coupling is a hot topic because it offers a path to sort electrons by their spin, a necessary feature of spin-based electronics. But the path is not easy to find or follow. Despite its ubiquity, Spin–orbit coupling rarely shows up in an exploitable way. In many crystals, two symmetries, time-reversal and inversion, ensure that spin-up and spin-down electrons are degenerate.

Even when an applied field or a crystal’s structure breaks one of the symmetries, another obstacle blocks the path. Spin is not conserved inside a crystal. Although the net spin polarization averages to zero, it fluctuates randomly and locally as electrons make their way through the crystal.

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