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 (e.g., a quantum dot) which can be modeled by a two-level Hamiltonian. We assume that a constant magnetic field B-0 acts on the spin, that electrons in the leads are in a voltage driven thermal equilibrium, and that the tunneling electrons are coupled to the spin through exchange and spin-orbit interactions. Using the nonequilibrium Keldysh formalism we find the dependence of the spin-spin and current-current correlation functions on the applied voltage between leads V, temperature T, B-0, and on the degree and orientation m(alpha) of spin polarization of the electrons in the right (alpha=R) and left (alpha=L) leads. We show the following (a) The spin-spin correlation function exhibits a peak at the Larmor frequency, omega(L), corresponding to the effective magnetic field B acting upon the spin as determined by B-0 and the exchange field induced by tunneling of spin-polarized electrons. (b) If the m(alpha)'s are not parallel to B the second-order derivative of the average tunneling current I(V) with respect to V is proportional to the spectral density of the spin-spin correlation function, i.e., exhibits a peak at the voltage V=homega(L)/e. (c) In the same situation when V>B the current-current correlation function exhibits a peak at the same frequency. (d) The signal-to-noise (shot-noise) ratio R for this peak reaches a maximum value of order unity, Rless than or equal to4, at large V when the spin is decoupled from the environment and the electrons in both leads are fully polarized in the direction perpendicular to B. (e) R<1 if the electrons are weakly polarized, or if they are polarized in a direction close to B-0, or if the spin interacts with the environment stronger than with the tunneling electrons. Our results of a full quantum-mechanical treatment of the tunneling-via-spin model when V>B are in agreement with those previously obtained in the quasiclassical approach. We discuss also the experimental results observed using scanning tunneling microscopy dynamic probes of the localized spin.