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We studied the quantum critical behavior of the second antiferromagnetic (AF)phase in the heavily electron-doped high-$T_c$ pnictide, LaFeAsO$_{1-x}$H$_x$by using $^{75}$As and $^{1}$H nuclear-magnetic-resonance (NMR) technique. Inthe second AF phase, we observed a spatially modulated spin-density-wave-likestate up to $x$=0.6 from the NMR spectral lineshape and detected a low-energyexcitation gap from the nuclear relaxation time $T_1$ of $^{75}$As. Theexcitation gap closes at the AF quantum critical point (QCP) at $x \approx0.49$. The superconducting (SC) phase in a lower-doping regime contacts thesecond AF phase only at the AF QCP, and both phases are segregated from eachother. The absence of AF critical fluctuations and the enhancement of thein-plane electric anisotropy are key factors for the development ofsuperconductivity.

Quantum critical behavior in heavily doped LaFeAsO$_{1-x}$H$_x$ pnictide superconductors analyzed using nuclear magnetic resonance