  This work considers the g-tensor anisotropy induced by the flexural thermal
vibrations in one-dimensional structures and its role in electron spin
relaxation. In particular, the mechanism of spin-lattice relaxation via
flexural modes is studied theoretically for localized and delocalized
electronic states in semiconducting carbon nanotubes in the presence of
magnetic field. The calculation of one-phonon spin-flip process predicts
distinctive dependencies of the relaxation rate on temperature, magnetic field
and nanotube diameter. Comparison with the spin relaxation caused by the
hyperfine interaction clearly suggests the relative efficiency of the proposed
mechanism at sufficiently high temperatures. Specifically, the longitudinal
spin relaxation time in the semiconducting carbon nanotubes is estimated to be
as short as 30 microseconds at room temperature.
