Spin-vibron coupling effects in single-molecule magnets grafted to a nanoelectromechanical system

Abstract

We present a theoretical analysis of the interplay between the spin-vibron and electron-vibron interactions in a hybrid system made of a single-molecule magnet and a suspended conductor. The latter is coupled to particle reservoirs and supports quantized vibrational modes which, once activated, interact with the localized magnetic moment $S$ of the nanomagnet. The dynamics of the molecular spin, the average vibron number, and the transient currents are calculated from the reduced density operator of the hybrid system. We focus on the effect of the vibron-assisted transitions from the lowest energy spin doublet ${S}_{z}=\ifmmode\pm\else\textpm\fi{}S$ to higher energy excited states. The numerical simulations performed for the simplest case $S=2$ prove that the vibron-assisted spin transitions and dynamics can be described in terms of a three-level $\mathrm{\ensuremath{\Lambda}}$ model borrowed from quantum optics. In particular we predict the existence of Rabi oscillations of the transient currents as fingerprints of the spin-vibron coupling. The role of symmetric or asymmetric bias configurations in setting different mixtures of molecular spin states in the steady-state regime is also emphasized.