We investigate cooling of a vibrational mode of a magnetic quantum dot by a spin-polarized tunneling charge current exploiting the magnetomechanical coupling. The spin-polarized current polarizes the magnetic nanoisland, thereby lowering its magnetic energy. At the same time, Ohmic heating increases the vibrational energy. A small magnetomechanical coupling then permits us to remove energy from the vibrational motion and cooling is possible. We find a reduction of the vibrational energy below 50% of its equilibrium value. The lowest vibration temperature is achieved for a weak electron-vibration coupling and a comparable magnetomechanical coupling. The cooling rate increases at first with the magnetomechanical coupling and then saturates.

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.

We investigate the current noise of nanoelectromechanical systems close to a continuous mechanical instability. In the vicinity of the latter, the vibrational frequency of the nanomechanical system vanishes, rendering the system very sensitive to charge fluctuations and, hence, resulting in very large (super-Poissonian) current noise. Specifically, we consider a suspended single-electron transistor close to the Euler buckling instability. We show that such a system exhibits an exponential enhancement of the current noise when approaching the Euler instability which we explain in terms of telegraph noise.

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