Incommensurate spin-density wave and a multiband superconducting phase in Na${}_x$FeAs revealed by nuclear magnetic resonance

We report a ${}^{23}$Na and ${}^{75}$As nuclear magnetic resonance (NMR) investigation of Na${}_x$FeAs series ($x=1$, $0.9$, $0.8$) exhibiting a spin-density-wave (SDW) order below $T_{\mathrm{SDW}}=45$, 50, and 43 K for $x=1$, $0.9$, $0.8$, respectively, and a bulk superconductivity below $T_c\approx 12$ K for $x=0.9$. Below $T_{\mathrm{SDW}}$, a spin-lattice relaxation reveals the presence of gapless particle-hole excitations in the whole $x$ range, meaning that a portion of the Fermi surface remains gapless. The superconducting fraction as deduced from the bulk susceptibility scales with this portion, while the SDW order parameter as deduced from the NMR linewidth scales inversely with it. The NMR line shape can only be reproduced assuming an incommensurate (IC) SDW. These findings qualitatively correspond to the mean-field models of competing interband magnetism and intraband superconductivity, which lead to an IC SDW order coexisting with superconductivity in part of the phase diagram.

Figure 1

(Color online) Room-temperature XRD of Na${}_1$FeAs sample. All peaks can be indexed to the $P4/nmm$ space group showing that the sample does not contain any impurity phases. Inset: Comparison of Na${}_x$FeAs ($x=1$, $0.9$, $0.8$) XRDs showing that the three samples are isostructural.

Figure 2

(Color online) (a) ${}^{23}$Na NMR spectra of powdered Na${}_x$FeAs samples ($x=1$, $0.9$, $0.8$) at 300 K. (b) ${}^{23}$Na NMR spectra of Na${}_1$FeAs at 60 and 30 K (thick green lines). Comparison is made to the simulated spectra for a powdered sample with ${\nu }_Q=530$ kHz and with the following type of the SDW order: no order (thin dotted line), IC SDW with the order parameter $0.28{\mu }_B$ (thin solid line), commensurate SDW with the order parameter $0.28{\mu }_B$ (thin dashed line) and commensurate SDW with the order parameter $0.12{\mu }_B$ (thin short dashed line). (c) Temperature dependence of the width of ${}^{23}$Na central transition in the three samples.

Figure 3

(Color online) (a) Temperature dependence of the dc spin susceptibility in Na${}_x$FeAs samples for $x=1$, $0.9$, $0.8$. (b) Temperature dependence of ${}^{23}$Na $1/T_{1}T$ measured in Na${}_x$FeAs samples. The ${}^7$Li data measured in Li${}_1$FeAs are added for comparison. Arrows indicate the SC (dashed) and the SDW (solid) transition temperatures. Solid and dashed lines are fits to Eqs. (1) and (2), respectively. Inset shows the dependence of ${}^{23}$Na $T_1\left(T_c\right)/T_1$ on $T_c/T$. The rate of suppression is significantly smaller than BCS or even unconventional $T^3$ behavior. (c) Temperature dependence of the stretching exponent $\gamma$ used in extracting the ${}^{23}{T}_1$ values from the spin-lattice relaxation data. Dashed lines indicate the temperature independent values $\sim$0.55 and $\sim$0.74 adopted by all three Na${}_x$FeAs samples below and above the corresponding $T_{\mathrm{SDW}}$, respectively.

Figure 4

(Color online) ${}^{75}$As NMR spectra of powdered Na${}_1$FeAs at 70, 50, 40, and 35 K (thick green lines). Comparison is made to the simulated spectra for a powdered sample with $\eta =0$ at 70 K (thin black line), $\eta =0$ (thin gray line) and $0.1$ (thin black line) at 50 K (with six-times magnified high-frequency singularity belonging to the satellite transition in the inset), and $\eta =0.15$ at 40 and 35 K. At 40 K the following type of the SDW order is assumed: commensurate SDW (dashed thin gray line), disordered version of the commensurate SDW (solid thin gray line), and sinusoidal IC SDW (solid thin black line). At 35 K a distorted sinusoidal IC SDW (solid thin black line) is assumed. The details are in the text.