Theory of magnetoresistance due to lattice dislocations in face-centred cubic metals

Abstract

A theoretical model to describe the low temperature magneto-resistivity of high purity copper single and polycrystals containing different density and distribution of dislocations has been developed. In the model, magnetoresistivity tensor is evaluated numerically using the effective medium approximation. The anisotropy of dislocation-induced relaxation time is considered by incorporating two independent energy bands with different relaxation times and the spherical and cylindrical Fermi surfaces representing open, extended and closed electron orbits. The effect of dislocation microstructure is introduced by means of two adjustable parameters corresponding to the length and direction of electron orbits in the momentum space, which permits prediction of magnetoresistance of FCC metals containing different density and distribution of dislocations. The results reveal that dislocation microstructure influences the character of the field-dependent magnetoresistivity. In the orientation of the open orbits, the quadratic variation in magnetoresistivity changes to quasi-linear as the density of dislocations increases. In the closed orbit orientation, dislocations delay the onset of magnetoresistivity saturation. The results indicate that in the open orbit orientations of the crystals, the anisotropic relaxation time due to small-angle dislocation scattering induces the upward deviation from Kohler’s rule. In the closed orbit orientations Kohler’s rule holds, independent of the density of dislocations. The results obtained with the model show good agreement with the experimental measurements of transverse magnetoresistivity in deformed single and polycrystal samples of copper at 2 K.