Linear response results for phonons and electron-phonon coupling in hexagonal close packed Sc-spin fluctuations, and implications for superconductivity

摘要

We present a FP-LMTO (full-potential linear muffin-tin orbital) study of the variation in the electronic structure, phonon frequencies and electron-phonon coupling in hexagonal close packed (hcp) Sc under pressure. The electron-phonon coupling constant lambda is found to increase steadily with pressure in the hcp phase, until the pressure reaches a value where the hcp phase becomes unstable. Linear response calculations for the normal pressure c/a ratio predict a phase change somewhere between calculated pressures of 22 and 30 GPa. The calculated frequencies for the equilibrium hcp lattice parameters are in good agreement with the inelastic neutron scattering results. There is a small upward shift in the Gamma-point E-2g mode frequency under pressure, in qualitative agreement with the Raman spectroscopy study of Olijnyk et al (2006 J. Phys.: Condens. Matter 18 10971). From the measured value of the electronic specific heat constant and the calculated values of the Fermi level density of states and electron-phonon coupling constant, we conclude that the electron-paramagnon coupling constant in hcp Sc should be comparable to the electron-phonon coupling constant. This indicates that the spin fluctuation effects are strong enough to suppress superconductivity completely in hcp Sc. We argue that spin fluctuations should be reduced by a factor of two or more in the high pressure Sc-II phase. On the basis of estimates of the electron-paramagnon coupling constants and the calculated or estimated electron-phonon coupling constants, we argue that the hcp phase may become superconducting with a very low transition temperature immediately prior to the transition to the Sc-II phase and that the Sc-II phase should indeed be superconducting. The electronic, electron-phonon and spin fluctuation properties of hcp Sc under pressure are compared with those of the high pressure hcp phase of Fe, which was reported to be superconducting a few years back.