  We investigate the total spin in an individual single-wall carbon nanotube
quantum dot with various numbers of electrons in a shell by using the ratio of
the saturation currents of the first steps of Coulomb staircases for positive
and negative biases. The current ratio reflects the total-spin transition that
is increased or decreased when the dot is connected to strongly asymmetric
tunnel barriers. Our results indicate that total spin states with and without
magnetic fields can be traced by this method.
