  We investigate the role played by the electron spin and the spin-orbit
interaction on the exceptional electronphonon coupling at the Tl/Si(111)
surface. Our first-principles calculations demonstrate that the particular spin
pattern of this system dominates the whole low-energy electron-phonon physics,
which is remarkably explained by forbidden spin-spin scattering channels. In
particular, we show that the strength of the electron-phonon coupling appears
drastically weakened for surface states close to the K and K' valleys, which is
unambiguously attributed to the spin polarization through the associated
modulation due to the spinor overlaps. However, close to the {\Gamma} point,
the particular spin pattern in this area is less effective in damping the
electron-phonon matrix elements, and the result is an exceptional strength of
electron-phonon coupling parameter {\lambda} ~ 1.4. These results are
rationalized by a simple model for the electron-phonon matrix elements
including the spinor terms.
