Tunneling measurement of quantum spin oscillations

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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 B₀ 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, B₀, and on the degree and orientation mα of spin polarization of the electrons in the right (α=R) and left (α=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.