Conduction-Electron Spin Relaxation by Transition-Element Impurities in Copper

Abstract

Gossard et al. have recently measured the conduction‐electron spin‐flip cross sections ${\sigma }_{\mathrm{sf}}$ of the transition elements Ti, Mn, and Ni in Cu. We give here an interpretation of these measurements based on the Anderson‐Friedel theory of localized virtual states. ${\sigma }_{\mathrm{sf}}$ is found to be proportional to the square of the $d$ density of states at the Fermi level and to the square of the spin‐orbit coupling which is modified by an orbital enhancement factor. Thus as one moves across the transition series, the variation of ${\sigma }_{\mathrm{sf}}$ should show a qualitative resemblance to that of the residual resistivity $\rho$ , and in particular show a minimum at Mn, in agreement with experiment. The precise variation of ${\sigma }_{\mathrm{sf}}$ is more pronounced and more asymmetric with respect to $\mathrm{Mn}$ than that of $\rho$ . Inclusion of the crystal‐field splitting affects greatly the calculated value of ${\sigma }_{\mathrm{sf}}$ for Ni and it is concluded that the splitting for Ni must be very small or inverted. Assuming $\mathrm{U}\text{\hspace{0.17em}=\hspace{0.17em}3\hspace{0.17em}}\mathrm{eV}$ and $\text{J\hspace{0.17em}=\hspace{0.17em}0.5\hspace{0.17em}}\mathrm{eV}$ , it is found that the values of the virtual level half‐width $\Delta$ needed to make the calculated ${\sigma }_{\mathrm{sf}}$ agree with experiment are $\text{Δ\hspace{0.17em}=\hspace{0.17em}1.0\hspace{0.17em}}\mathrm{eV}$ for Ti and $\text{Δ\hspace{0.17em}=\hspace{0.17em}0.3\hspace{0.17em}}\mathrm{eV}$ for Ni.