Anomalous Electrical Resistivity and Magnetoresistance Due to an s − d Interaction in Cu-Mn Alloys

The effect of the $s\ensuremath{-}d$ exchange interaction between the conduction electrons and the Mn ions on the electrical behavior of Cu-Mn alloys is investigated from the molecular-field point of view. The magnitude of the anomalous resistivity calculated with the value of the exchange integral for a free ${\mathrm{Mn}}^{+}$ ion agrees with the experimental value within a factor of three. Also the temperature dependence of the resistivity obtained by the molecular-field approximation for the antiferromagnetic spin ordering is shown to be quite similar to the behavior exhibited by the alloys with more than one atomic percent Mn. For samples with lower concentration of Mn ions, however, the theoretical result shows only a monotonic decrease of the resistance below the N\'eel temperature. It shows neither the resistance minimum nor maximum which has been found experimentally for the very dilute alloys. The anomalous magnetoresistance calculated on the same basis is approximately proportional to the square of the magnetization and its magnitude is in good agreement with the experimental results, especially above the N\'eel temperature. The magnetoresistance of ferromagnetic metals is also discussed.