  We report on the giant magnetoresistance (GMR) of multiwall carbon nanotubes
with ultra small diameters. In particular, we consider the effect of the
inter-wall interactions and the lead/nanotube coupling. Comparative studies
have been performed to show that in the case when all walls are well coupled to
the electrodes, the so-called inverse GMR can appear. The tendency towards a
negative GMR depends on the inter-wall interaction and on the nanotube le ngth.
If, however, the inner nanotubes are out of contact with one of the electrodes,
the GMR remains positive even for relatively strong inter-wall interactions
regardless of the outer nanotube length. These results shed additional light on
recently reported experimental data, where an inverse GMR was found in some
multiwall carbon nanotube samples.
