  We report on our theoretical study of the magnetoresistance in spin polarized
transport through a finite carbon nanotube (CNT). Varying the Fermi energy of a
CNT and the relative strength of couplings to two ferromagnetic (FM)
electrodes, we studied the conductance as well as the magnetoresistance (MR).
Due to resonant transport through discrete energy levels in a finite CNT, the
conductance and MR are oscillating as a function of the CNT Fermi energy. The
MR is peaked at the conductance valleys and dipped close to the conductance
peaks. When couplings to two FM electrodes are asymmetric, the MR dips become
negative under a rather strong asymmetry. When couplings are more or less
symmetric, the MR dips remain positive except for a very strong coupling case.
Under strong coupling case, the line broadening is significant and transport
channels through neighboring energy levels in a CNT interfere with each other,
leading to the negative MR.
