Measurements of the electron-phonon interaction in Nb by inelastic neutron scattering

Abstract

Precise linewidth and frequency measurements of transverse acoustic modes propagating along the [001] and [110] directions were performed on single crystals of niobium in the normal and superconducting phases (${T}_{c}=9.2\ifmmode^\circ\else\textdegree\fi{}$K). For transverse phonons propagating along the [110] direction changes in linewidth are observed when the superconducting gap $2\ensuremath{\Delta}(T)$ equals the phonon frequency. This behavior agrees with Bobetic's calculation for the attenuation of high-frequency sound waves in superconductors and the magnitude of the change enables us to calculate the electron-phonon interactions. In addition to linewidth changes, anomalous temperature dependence of the peak position of some acoustic modes is also observed. The [001] transverse phonons exhibit a decrease of \ensuremath{\sim} 15% when $T$ is decreased from 300\ifmmode^\circ\else\textdegree\fi{}K to ${T}_{c}$. Below ${T}_{c}$ there is an additional softening of 3%. This softening extends along the $[\ensuremath{\zeta}00]$ direction to $\ensuremath{\zeta}=0.5$, the limit of our measurements.