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Recent experiments in ferromagnetic atomic-sized contacts have shown that the anisotropic magnetoresistance (AMR) is greatly enhanced and has an asymmetric angular dependence as compared with that of bulk samples. The origin of these effects is still under debate. In this work we present a theoretical analysis of the AMR in atomic contacts of the 3d ferromagnetic materials. Our results strongly suggest that the anomalous AMR stems from the reduced symmetry of the atomic contact geometries. We also present calculations supporting the idea that the pronounced voltage- and temperature dependence in some experiments can be attributed to impurities near the constrictions.

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