Origin of the Pressure-Induced Volume Collapse in Tb

The mechanism responsible for the high-pressure volume collapse in most elemental rare-earth metals is still a matter of debate. Models attempting to explain this collapse include: (i) valence transition, (ii) 4$f$ local-to-band transition (Mott-Hubbard), (iii) $f$-$d$ hybridization (Kondo), and (iv) \textit{sp}$\to d$ transfer. We focus on Tb metal which displays a 5{\%} volume collapse at 53 GPa. X-ray absorption spectroscopy shows persistence of Tb's 4$f^{\mathrm{8}}$ state across the volume collapse, excluding (i) as a mechanism. Furthermore, x-ray emission spectroscopy shows that 4$f$ states retain their localized nature to at least 70 GPa, ruling out (ii). On the other hand, the suppression of the x-ray absorption ``white line'' with pressure indicates that \textit{sp}$\to d$ transfer is active. To probe for Kondo interactions, the pressure dependence of the superconducting $T_{\mathrm{c}}$ in pure Y is compared to that in a Y(0.5 at{\%} Tb) alloy. We observe a strong suppression of $T_{\mathrm{c}}$ at pressures near terbium's volume collapse, an indication of a rapid increase of the Kondo temperature, in agreement with (iii). We argue that a Kondo model in the presence of \textit{sp}$\to d$ transfer best describes the volume collapse in Tb metal.