Tunneling measurement of quantum spin oscillations

We consider the problem of tunneling between two leads via a localized spin 1/2 or any other microscopic system which can be modeled by a two-level Hamiltonian. We assume that a constant magnetic field ${\bf B}_0$ acts on the spin, that electrons in the leads are in the thermal equilibrium and that the tunneling electrons are coupled to the spin through exchange and spin-orbit interactions. Using the non-equilibrium Keldysh formalism we find the dependence of the spin-spin and current-current correlation functions on the applied voltage between leads $V$, temperature $T$, ${\bf B}_0$, and on the degree and orientation ${\bf m}_{\alpha}$ of spin polarization of the electrons in the right ($\alpha=$R) and left ($\alpha=$L) leads. We compare our results of a full quantum-mechanical treatment of the tunneling-via-spin model with those previously obtained in the quasi-classical approach, and discuss the experimental results observed using STM dynamic probes of the localized spin.