Galvanomagnetic Effects, Magnetostriction, and Spin-Orbit Interaction in Cu-Ni-Fe and Other Ferromagnetic Nickel Alloys

Abstract

In the triangular diagram of Cu-Ni-Fe alloys, the line of zero linear magnetostriction ${\ensuremath{\lambda}}_{s}$ 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" $\frac{({\ensuremath{\rho}}_{\mathrm{II}}\ensuremath{-}{\ensuremath{\rho}}_{\ensuremath{\perp}})}{{\ensuremath{\rho}}_{0}}$ of quenched Cu-Ni-Fe alloys containing more than 60 wt% Ni has been measured at 20\ifmmode^\circ\else\textdegree\fi{}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 ${\ensuremath{\lambda}}_{s}=0$ 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 ${\ensuremath{\gamma}}_{{H}_{s}}=\frac{{R}_{s}{M}_{s}}{{\ensuremath{\rho}}^{2}}$ is roughly proportional to the magnetostriction ${\ensuremath{\lambda}}_{s}$ for all fcc Ni-Fe, Cu-Ni, and Cu-Ni-Fe alloys at $T\ensuremath{\ll}{T}_{c}$, with a slope \ensuremath{\approx}2.0\ifmmode\times\else\texttimes\fi{}${10}^{+9}$ mks.