  We study theoretically nonlocal spin transport in a ballistic carbon nanotube
contacted to two ferromagnetic leads and two normal-metal leads. When the
magnetizations of the two ferromagnets are changed from a parallel to an
antiparallel configuration, the circuit shows a hysteretic behavior which is
specific to the few-channel regime. In the coherent limit, the amplitude of the
magnetic signals is strongly enhanced due to resonance effects occurring inside
the nanotube. Our calculations pave the way for experiments on low-dimensional
nonlocal spin transport, which should give results remarkably different from
the experiments realized so far in the multichannel diffusive incoherent
regime.
