Elementary excitations and elusive superconductivity in palladium hydride -- \textit{ab initio} perspective. I. Paramagnons

\newcommand{\el}{\textit{et~al}.} Motivated by a experimental reports on possible high temperature superconductivity in palladium hydride [Tripodi \el, \textit{Physica C} \textbf{388-389}, 571 (2003)], we present a first principle study of spin fluctuations, electron-phonon coupling and critical temperature in PdH$_{x}$, $0 \leq x \leq 1$. A prerequisite for any qualitative study of exchange-enhanced materials is the knowledge of spin flip fluctuation spectrum. It is generally believed [Berk \& Schrieffer, \textit{Phys. Rev. Lett.}, \textbf{17}, 433 (1966)] that the ferromagnetic-like paramagnons of Pd are destructive for the conventional, i.e.\ $s$-wave, superconductivity. We describe them using linear response time dependent density functional theory, recently implemented to study complex metals [Buczek \el, \textit{Phys. Rev. Lett.} \textbf{105}, 097205 (2010)] . We find that hydrogenation suppresses the intense spin fluctuations of pure Pd, driving it away from a magnetic critical point. Under the assumption of $s$-wave pairing, this could lead to the formation of the superconducting state. The \textit{ab-initio} estimated electron-phonon coupling is strong enough to support superconductivity. Please look for the complementary contribution of Christophe Bersier.