Spin vibronics in interacting nonmagnetic molecular nanojunctions

Abstract

We show that in the presence of ferromagnetic electronic reservoirs and spin-dependent tunnel couplings, molecular vibrations in nonmagnetic single molecular transistors induce an effective intramolecular exchange magnetic field. It generates a finite spin-accumulation and -precession for the electrons confined on the molecular bridge and occurs under (non)equilibrium conditions. The effective exchange magnetic field is calculated here to lowest order in the tunnel coupling for a nonequilibrium transport setup. Coulomb interaction between electrons is taken into account as well as a finite electron-phonon coupling. We show that for realistic physical parameters, an effective spin-phonon coupling emerges. It is induced by quantum many-body interactions, which are either electron-phonon or Coulomb-like. We investigate the precession and accumulation of the confined spins as function of bias-and gate-voltages as well as their dependence on the angle enclosed by the magnetizations between the left and right reservoir.

Relaxation dynamics in double-spin systems

“…where n + (ω) = [exp(ω/k B T ) − 1] denotes the Bose function and n − (ω) = n + (ω) + 1. Assuming that the two total spin values form a pseudospin-1/2, the oscillations can be seen as an electron spin precessing around an effective exchange field [47][48][49][51][52][53][54][55][56]. Such an analogy has also been observed in the context of quantum transport though spatially localized [50,57,58] and non-localized orbitals [59].…”

Iterative path-integral summations for the tunneling magnetoresistance in interacting quantum-dot spin valves

“…In the presence of the counting field, time translation invariance is broken and there is no simple frequency representation of ∆ −1 [η] similar to Eq. (18). However, since we are only interested in calculating the current (and not higher-order correlation functions), we can expand ∆ −1 [η] to linear order in η α at a single Trotter index m (that corresponds to the time t m at which the current is measured) and drop the counting field anywhere else.…”

“…The resulting expression for ∆ −1 [η] is given by Eq. (18) with Γ ασ being replaced by Γ ασ [1− iδt 2 η α (νδ ml −ν δ ml )]. Furthermore, we observe that multiplying ∆ −1 [η] − Σ C (s) in Eq.…”

“…For weak tunnel cou-plings between quantum dot and leads, a perturbation expansion in the tunnel coupling is possible for various regimes of transport and gate voltages. A calculation to first order in the tunnel-coupling strength is sufficient to reveal the existence of an exchange field induced by finite Coulomb interaction on the quantum dot 16,17 or to show that the ferromagnetic Anderson-Holstein model acquires an effective attractive Coulomb interaction 18 . It has been shown that the TMR through a quantum-dot spin valve to first-plus second-order in tunneling features a zerobias anomaly 19 that could be explained by the influence of sequential and cotunneling processes on accumulation and relaxation of the quantum spin.…”

Revealing attractive electron–electron interaction in a quantum dot by full counting statistics

“…} is the Fermi function of lead r. A spin opposite to σ is denoted by s . Moreover, we also account for spin relaxation by including the spin-flip rate G  in the master equation (6)- (9). Spin relaxation may originate from hyperfine interaction with a local nuclei bath [35][36][37][38].…”