  An iron-based superconductor LaFeAsO$_{1-x}$H$_x$ (0 $\leq x \leq$ 0.6)
undergoes two antiferromagnetic (AF) phases upon H doping. We investigated the
second AF phase ($x$=0.6) using NMR techniques under pressure. At pressures up
to 2 GPa, the ground state is a spin-density-wave state with a large gap;
however, the gap closes at 4.0 GPa, suggesting a pressure-induced quantum
critical point. Interestingly, the gapped excitation coexists with gapless
magnetic fluctuations at pressures between 2 and 4 GPa. This coexistence is
attributable to the lift up of the $d_{xy}$ orbital to the Fermi level, a
Lifshitz transition under pressure.

Superconductivity