Pressure Dependence of the Knight Shift in Al and Nb Metal

The pressure dependence of the Knight shift K of Al and Nb metals was measured with a digitally slaved signal averager. The maximum hydrostatic pressure utilized was 8000 kg/cm². The observed value of dlnK/dlnV is - 1.01±{}0.02 and - 0.29±{}0.02 for Al and Nb, respectively. Since it is essential to know the volume dependence of the (electron-electron-enhanced) spin susceptibility dlnχₛₚ*dlnV in order to analyze the observed dlnK/dlnV, the theoretical implication of the previously proposed methods to estimate dlnχₛₚ*dlnV was explored. The linearly temperature-dependent thermal expansion at low temperature αₑ gives rise to the volume dependence of electron-phonon-enhanced density of states at the Fermi surface. αₑ includes only a temperature-independent part of the enhancement factor 1+λ. The pressure dependence of the superconductor parameters renders the volume dependence of the density of the states clothed with a full electron-phonon interaction, which includes the temperature-independent part as well as a possible temperature-dependent part. A semiempirical scheme to deduce the volume dependence of 1+λ, the density of states for the bare electrons N(EF)BS, and the band-structure effective mass m* is proposed. These values are derived from the pressure dependence of the superconducting transition temperature and αₑ. The volume dependence of χₛₚ^* is deduced from dlnN(EF)BSdlnV by taking into account the effect of the electron-electron enhancement factor. The volume dependence of the density of wave function at the Fermi surface 〈|ψ(0)|²〉 was deduced for Al as dln〈|ψ(0)|²〉dlnV=-2.12. The volume dependence of the orbital Knight shift K₀ for Nb is estimated as dlnK₀dlnV0.4 (or 0.1). The possible origin of the discrepancy between the density of states derived from αₑ and from the pressure dependence of the superconductor parameters is discussed. The origin of inconsistency in the previously reported temperature dependence of K for Al is also suggested.