  We propose a scheme for spin-based detection of the bending motion in
suspended carbon-nanotubes, using the curvature-induced spin-orbit interaction.
We show that the resulting effective spin-phonon coupling can be used to
down-convert the high-frequency vibration-modulated spin-orbit field to
spin-flip processes at a much lower frequency. This vibration-induced
spin-resonance can be controlled with an axial magnetic field. We propose a
Pauli spin blockade readout scheme and predict that the leakage current shows
pronounced peaks as a function of the external magnetic field. Whereas the
resonant peaks allow for frequency readout, the slightly off-resonant current
is sensitive to the vibration amplitude.
