Magnetoresistance of a Permalloy Single Crystal and Effect of3dOrbital Degeneracies

The electrical resistance of single crystals of the alloy 15% Fe-85% Ni has been measured at 20, 77, and 299°K, in a transverse or longitudinal magnetic field sufficient to cause ferromagnetic saturation. The current is parallel to a $〈100〉$, $〈110〉$, or $〈111〉$ direction. At 20°K, a change in orientation of the magnetization causes changes of resistivity reaching 30%. The temperature variation of the phenomenological Döring coefficients $k_1-k_5$ follows largely from their dependence on the type of scattering centers; the coefficients are large and positive in the case of impurity scattering alone, and are small or slightly negative in the case of phonon or magnon scattering alone. A microscopic theory has also been developed according to which conduction electrons are scattered by impurities into near-degenerate $3d$ states; these states are strongly perturbed and mixed by the interaction $A{L}_z{S}_z$. The perturbation of a near-degenerate pair of states is found to be highly anisotropic, and is possible only along a certain "polarization axis." Two different models reproduce correctly most features of the experimental data and are consistent with cubic symmetry. In the first model, the polarization axes are assumed to be parallel to the fourfold cubic axes of the crystal, and spin-orbit perturbation is assumed to decrease the probability of being scattered into a state of the pair. In the other model, the polarization axes are along the threefold cubic axes, and spin-orbit interaction increases the scattering probability. In both models, it is necessary to assume that the spin-orbit perturbation of a pair is large and nonlinear (because of the near degeneracy), in such a way that it tends to saturate at an almost constant value. Calculations of impurity scattering are made in the Slater-Koster approximation. The theory is then extended to show that the validity and success of these two models is actually independent of whether the $A{L}_z{S}_z$ interaction or the $A (L_x{S}_x+L_y{S}_y)$ interaction is the perturbing agent.