Spin-Orbit Scattering and Time-Reversal Symmetry: Detection of a Spin by Tunneling

We consider the possibility of detecting spin precession in a magnetic field by nonequilibrium transport processes. We find that time reversal symmetry imposes strong constraints on the problem. Suppose the tunneling occurs directly between systems at two different chemical potentials, rather than sequentially via a third system at an intermediate chemical potential. Then, unless the magnetic fields are extremely strong or spin polarized electrons are used, the periodic signal in the current results from beating together two different precession frequencies, so that observing a signal near the Larmor frequency in this case requires having some cluster with a $g$ factor close to zero.