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

Abstract

Gossard et al. have recently measured the conduction-electron spin-flip cross sections σsf 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. σsf 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 σsf should show a qualitative resemblance to that of the residual resistivity ρ, and in particular show a minimum at Mn, in agreement with experiment. The precise variation of σsf is more pronounced and more asymmetric with respect to Mn than that of ρ. Inclusion of the crystal-field splitting affects greatly the calculated value of σsf for Ni and it is concluded that the splitting for Ni must be very small or inverted. Assuming U = 3 eV and J = 0.5 eV, it is found that the values of the virtual level half-width Δ needed to make the calculated σsf agree with experiment are Δ = 1.0 eV for Ti and Δ = 0.3 eV for Ni.