  We investigated the mean-free path effects on the magnetoresistance of
ferromagnetic nanocontacts. For most combinations of parameters the
magnetoresistance monotonously decreases with increasing the contact
cross-section. However, for a certain choice of parameters the calculations
show non-monotonous behavior of the magnetoresistance in the region in which
the diameter of the contact becomes comparable with the mean-free path of
electrons. We attribute this effect to different conduction regimes in the
vicinity of the nanocontact: ballistic for electrons of one spin projection,
and simultaneously diffusive for the other. Furthermore, at certain
combinations of spin asymmetries of the bulk mean-free paths in a
heterocontact, the magnetoresistance can be almost constant, or may even grow
as the contact diameter increases. Thus, our calculations suggest a way to
search for combinations of material parameters, for which high
magnetoresistances can be achieved not only at the nanometric size of the
contact, but also at much larger cross-sections of nanocontacts which can be
easier for fabrication with current technologies. The trial calculations of the
magnetoresistance with material parameters close to those for the Mumetal-Ni
heterocontacts agree satisfactorily with the available experimental data.
