Ballistic versus diffusive magnetoresistance of a magnetic point contact

The quasiclassical theory of a nanosize point contacts (PC's) between two ferromagnets is developed. The maximum available magnetoresistance values in PC's are calculated for ballistic versus diffusive transport through the area of a contact. In the ballistic regime the magnetoresistance in excess of a few hundred percent is obtained for the iron-group ferromagnets. The necessary conditions for realization of so large a magnetoresistance in PC's, and the experimental results by Garc\'{\i}a et al. are discussed.