Spin-vibration interaction in a nanomechanical spin-valve

We study spin-dependent transport in a suspended carbon nanotube quantum dot in contact with two ferromagnetic leads and with the dot’s spin coupled to the flexural modes. We consider a spinvibrational interaction inducing spin-flip processes between the two Zeeman levels of the dot due to spin-orbit interaction or a magnetic field gradient. The inelastic vibration-assisted spin-flips give rise to a mechanical damping and for an applied bias-voltage to a steady non-equilibrium occupation of the harmonic oscillator. We discuss how these effects depend on the Zeeman splitting and the magnetic polarization of the leads. Depending on the magnetic configuration and the bias voltage polarity, the vibration can be cooled or become unstable. Owing to the sensitivity of the electron transport to the spin orientation, we find signatures of the nanomechanical motion in the currentvoltage characteristic even for weak spin-vibrational coupling. Hence, the vibrational state can be read out in the current-voltage characteristic.