Multivalued dependence of the magnetoresistance on the quantized conductance in nanosize magnetic contacts

We calculate the quantized conductance of nanosize point contacts between two ferromagnets for different mutual orientations of the magnetic moments. It is found that the magnetoresistance MR is a multivalued function of the quantized conductance at the parallel alignment of the magnetizations sigma^F. This leads us to the conclusion that experimentally observed large fluctuations of MR versus sigma^F are rather due to the conductance quantization than to measurement errors or a poor reproducibility of the results. Using the results of the calculations we are able to understand experimental data obtained by Garcia et al for MR of the magnetic nanocontacts.