Magnetoresistance of a Permalloy Single Crystal
Authors: Berger L. , Friedberg S. A. 
Published: January 2006

Measurements of magnetoresistance in nickel alloys may be used as a tool to study the perturbation of 3d states by spin-orbit interaction. This method has the advantage of providing a very narrow energy window, looking selectively at the states located at the Fermi level (from that point of view, the analysis of measurements of other quantities depending on spin-orbit interaction, such as the magnetocrystalline anisotropy or the gyromagnetic ratio, is not so simple since all states below the Fermi level contribute in that case). The alloy 15% Fe-85% Ni is probably one of the most suitable materials, since the effects are largest; previous work on magnetoresistance, Hall effect, and magnetostriction of polycrystals of this alloy has suggested the presence of near-degenerate pairs of states at the Fermi level.
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 Döring coefficients k1, k2, k3, k4, k5 have been determined at 20°, 77°, 299°K, by fitting the phenomenological Döring expression to the experimental data. By using a relation based on Matthiessen's rule, it is possible to extrapolate the values of the Döring coefficients to the case of impurity scattering alone and to the case of phonon scattering alone. The coefficients are large and positive in the first case, and are small or slightly negative in the second case.
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 LzSz. The perturbation of a near-degenerate pair of states is found to be highly anisotropic. The theory formulates all spin-orbit properties of a pair ψa and ψb terms of an “orbital polarization axis” m defined by m = (1/i) 〈ψa | L | ψb〉, without having to specify further the nature of the pair. It can be shown that the perturbation and mixing of the states of the pair by the interaction A LzSz depends only on the square of the component of the spin S along m, and is maximum when S is parallel to m. On the other hand, if the perturbation is caused by A (LxSx+LySy), the effect is maximum when S is perpendicular to m. We compute the resistivity for arbitrary directions of S and of the current. Impurity s-d scattering is treated in the Slater-Koster approximation. Two different models reproduce correctly most features of the experimental data. 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 perturbation of a pair is large and nonlinear (due to the near-degeneracy), in such a way that it tends to saturate at an almost constant value. The gap between unperturbed pair components is of order 0.1 eV. It is shown that the validity and success of these two models is actually independent of whether the A LzSz interaction or the A (LxSx+LySy) interaction is the perturbing agent.
An extensive publication appears in Phys. Rev. 165, 670 (1968).