In the triangular diagram of Cu-Ni-Fe alloys, the line of zero linear magnetostriction ${\lambda }_s$ approximately coincides with the line of zero extraordinary Hall constant $R_s$ and may be interpreted as the line where a $3d$ orbital degeneracy crosses the Fermi level. The "ferromagnetic anisotropy of resistivity" $\frac{({\rho }_{\mathrm{II}}-{\rho }_{\perp })}{{\rho }_0}$ of quenched Cu-Ni-Fe alloys containing more than 60 wt% Ni has been measured at 20°K, where impurity scattering dominates. The large anisotropy values observed in Ni-Fe alloys decrease gradually by addition of copper. In particular, the anisotropy decrease along the line ${\lambda }_s=0\mathrm{}$ suggests that the orbital degeneracy is partially lifted by the addition of copper. This line differs from a line of constant electron concentration, indicating a departure from the rigid-band model. A $3d$ band model with separate iron, nickel, and copper sub-bands correctly predicts the location of the line if the degeneracy is assumed to be located at the top of the nickel sub-band (bottom of the iron sub-band). The same assumption applies successfully to Me-Ni-Fe alloys, where Me is any metal (Cr, W, Mo, V, etc.) forming a nonmagnetic sub-band above the Fermi level. Existing data show that the extraordinary Hall conductivity ${\gamma }_{H_s}=\frac{R_s{M}_s}{{\rho }^2}$ is roughly proportional to the magnetostriction ${\lambda }_s$ for all fcc Ni-Fe, Cu-Ni, and Cu-Ni-Fe alloys at $T\ll T_c$, with a slope ≈2.0×${10}^{+9\mathrm{}}$ mks.

• Received 1 April 1969

DOI:https://doi.org/10.1103/PhysRev.185.792