Cooling a magnetic nanoisland by spin-polarized currents

We investigate cooling of a vibrational mode of a magnetic quantum dot by a spin-polarized tunneling charge current, exploiting the interaction between the magnetization and the vibration. The spin-polarized charge current polarizes the magnetic nanoisland, lowering its energy. Inevitable Ohmic energy losses due to the charge current flow will heat up the vibration. A small but finite coupling between the vibration and the local magnetic moment then permits an energy exchange, resulting in a lower energy, i.e., cooling, of the vibrational mode. We determine parameter regimes for the cooling of the vibration below $50\%$ of its initial value. Lowest final phonon temperature is observed for weak electron-phonon-coupling but similar magnetization-phonon coupling strength. The cooling rate, thereby, increases at first with the magnetization-phonon coupling and then saturates.