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

We studied the quantum critical behavior of the second antiferromagnetic (AF) phase in the heavily electron-doped high-$T_c$ pnictide, ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$, by using a ${}^{75}\mathrm{As}$ and ${}^1\mathrm{H}$ nuclear magnetic resonance (NMR) technique. In the second AF phase, we observed a spatially modulated spin-density-wave-like state up to $x=0.6$ from the NMR spectral line shape and detected a low-energy excitation gap from the nuclear relaxation time $T_1$ of ${}^{75}\mathrm{As}$. The excitation gap closes at the AF quantum critical point (QCP) at $x\approx 0.49$. The superconducting phase in a lower-doping regime contacts the second AF phase only at the AF QCP, and both phases are segregated from each other. The absence of AF critical fluctuations and the enhancement of the in-plane electric anisotropy are key factors for the development of superconductivity.

Figure 1

Nuclear magnetic relaxation divided by temperature $1/T_{1}T$ for ${}^{75}\mathrm{As}$. $T_c$ indicated by up arrows are determined from the detuning of the NMR tank circuit. $T_N$ are determined from the maximum of $1/T_{1}T$ as shown by down arrows. The data for 20% and 40% H-doped samples are cited from Ref. [2]. The curves for each doping level are guides to the eye.

Figure 2

(a),(b) $1/T_{1}T$ in the antiferromagnetic (AF) and paramagnetic (PM) phases. The data at high temperatures are fitted to the Curie-Weiss law, and the data at low temperatures are fitted to Eq. (1). (c) $1/T_{1}T$ in the superconducting (SC) and PM phases. (d) Detuning of the NMR tank circuit. It is plotted as the resonance-frequency shift $\Delta f/f$. (e) $1/T_{1}T$ for the nondoped samples. The data were taken from Ref. [14].

Figure 3

${}^{75}\mathrm{As}$ and ${}^{139}\mathrm{La}$ NMR spectra measured at 35.1 MHz. (a) Spectra in the AF phases for ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{F}}_x$ and ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$. The illustration indicates powder patterns of the AF phase for the lightly F-doped samples. A part of the data for the F-doped samples is taken from Ref. [14]. (b),(c) Comparison of spectra between the AF and PM phases.

Figure 4

${}^1\mathrm{H}$ NMR spectra for 60% H-doped samples. (a) Spectra at several temperatures below and above $T_N\left(=100\mathrm{K}\right)$. (b) Comparison of ${}^1\mathrm{H}$ NMR spectra in ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ with ${}^{19}\mathrm{F}$ NMR spectra in ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{F}}_x$. (c) The ${}^1\mathrm{H}$ linewidth of ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ for several doping levels. The natural linewidth observed in a PM state was subtracted in the figure.

Figure 5

(a) Low-energy AF-excitation gap determined from Eq. (1) as a function of H concentration $x$. (b) Phase diagram of ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{F}}_x$ and ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$. The structural transition temperatures ($T_s$) [14, 21] and the antiferromagnetic (AF) transition temperatures ($T_N$) [4, 21] of ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{F}}_x$ are shown by open and closed squares, respectively. The superconducting transition temperatures ($T_c$) were determined from resistivity measurements (closed and open red circles) [1, 20], detuning of the NMR tank circuit (open red triangles), and $1/T_{1}T$ (closed red triangles). $T_N$ of ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ were determined from $1/T_{1}T$ (closed blue triangles) and the linewidth (closed blue squares). Pseudogap behavior is seen at temperatures below $T^{*}$. The yellow-shaded regime shows the enhancement of the in-plane electric-field-gradient anisotropy $\eta$.