Concentration dependence and temperature dependence of hydrogen tunneling in Nb(OH)x

Abstract

We have studied by neutron spectroscopy the concentration (1.5×${10}^{\mathrm{-}4}$≤x≤1.1×${10}^{\mathrm{-}2}$) and temperature dependence (0.5 K≤T≤10 K) of H tunneling in Nb(OH${)}_{\mathrm{x}}$. For T<5 K a narrow inelastic line is observed for x=1.5×${10}^{\mathrm{-}4}$ which changes into a broad peak at higher concentrations. This shows that interactions between the defects lead to a distribution of both the asymmetry of the potentials and the matrix element. Between 5 and 10 K the data reveal a renormalization of the matrix element and an increased damping due to a Korringa-type coupling of the tunnel system with conduction electrons.