Theory of the Anisotropic Magnetoresistance in Copper

The motion of the guiding center of magnetic circulation generates a charge transport. The application of kinetic theory to the motion gives a formula for the magnetoconductivity: $\sigma = e^2 n_{\mathrm{c}} \tau /M^*$, where $M^*$ is the magnetotransport mass distinct from the cyclotron mass, $n_{\mathrm{c}}$ the density of the conduction electrons, and $\tau$ the relaxation time. The density $n_{\mathrm{c}}$ depends on the applied magnetic field direction relative to copper's face-centered-cubic lattice, when the Fermi surface of copper is nonspherical with \emph{necks}. The anisotropic magnetoresistance of copper is calculated. A good fit with experiments is obtained.