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

Abstract

We present a FP-LMTO (full-potential linear muffin-tin orbital) study of the variation inthe electronic structure, phonon frequencies and electron–phonon coupling in hexagonalclose packed (hcp) Sc under pressure. The electron–phonon coupling constantλ is found to increase steadily with pressure in the hcp phase, until the pressure reaches a valuewhere the hcp phase becomes unstable. Linear response calculations for the normal pressurec/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 goodagreement with the inelastic neutron scattering results. There is a small upward shift in theΓ-pointE2g mode frequency under pressure, in qualitative agreement with the Raman spectroscopystudy of Olijnyk et al (2006 J. Phys.: Condens. Matter 18 10971). From the measured valueof the electronic specific heat constant and the calculated values of the Fermi leveldensity of states and electron–phonon coupling constant, we conclude that theelectron–paramagnon coupling constant in hcp Sc should be comparable to theelectron–phonon coupling constant. This indicates that the spin fluctuation effects arestrong enough to suppress superconductivity completely in hcp Sc. We argue that spinfluctuations 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 thecalculated or estimated electron–phonon coupling constants, we argue that thehcp phase may become superconducting with a very low transition temperatureimmediately prior to the transition to the Sc-II phase and that the Sc-II phaseshould indeed be superconducting. The electronic, electron–phonon and spinfluctuation properties of hcp Sc under pressure are compared with those of the highpressure hcp phase of Fe, which was reported to be superconducting a few yearsback.