Tunneling measurement of quantum spin oscillations

TL;DR

This paper models quantum spin oscillations during electron tunneling between leads, analyzing how various parameters affect spin and current correlations, and compares quantum and classical approaches with experimental observations.

Contribution

It provides a comprehensive quantum-mechanical analysis of tunneling via a localized spin, including effects of magnetic field, polarization, and voltage, extending previous quasi-classical models.

Findings

Dependence of correlation functions on voltage, temperature, and magnetic field.

Comparison showing quantum treatment differs from quasi-classical results.

Discussion of experimental STM observations of localized spins.

Abstract

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.