Spatial competition of the ground states in 1111 iron pnictides

Using nuclear quadrupole resonance, the phase diagram of $1111 R{\mathrm{FeAsO}}_{1-x}{\mathrm{F}}_x$ ($R=\text{La}$, Ce, Sm) iron pnictides is constructed as a function of the local charge distribution in the paramagnetic state, which features low-doping-like (LD-like) and high-doping-like (HD-like) regions. Compounds based on magnetic rare earths (Ce, Sm) display a unified behavior, and comparison with La-based compounds reveals the detrimental role of static iron $3d$ magnetism on superconductivity, as well as a qualitatively different evolution of the latter at high doping. It is found that the LD-like regions fully account for the orthorhombicity of the system, and are thus the origin of any static iron magnetism. Orthorhombicity and static magnetism are not hindered by superconductivity but limited by dilution effects, in agreement with two-dimensional (2D) (respectively three-dimensional) nearest-neighbor square lattice site percolation when the rare earth is nonmagnetic (respectively magnetic). The LD-like regions are not intrinsically supportive of superconductivity, contrary to the HD-like regions, as evidenced by the well-defined Uemura relation between the superconducting transition temperature and the superfluid density when accounting for the proximity effect. This leads us to propose a complete description of the interplay of ground states in 1111 pnictides, where nanoscopic regions compete to establish the ground state through suppression of superconductivity by static magnetism, and extension of superconductivity by proximity effect.

Figure 1

NQR spectra of the studied samples in the paramagnetic state. The doping is indicated as $x_{\text{NQR}}/x_{\text{FSWT}}$ (FSWT: full spectral weight transfer; see text). The measurement temperature is coded by the color (see also the scale in Fig. 3): Yellow for room temperature, magenta for 150–160 K, indigo for 100 K (Ce, $x_{\text{NQR}}/x_{\text{FSWT}}=0.63)$, blue for 40–55 K. Full lines are Gaussian fits. Some low-temperature La/Sm spectra are from a previous study [21].

Figure 2

Procedure to extract $x_{\text{NQR}}/x_{\text{FSWT}}$ for a sample with high-enough doping that a single NQR line is present, or for a sample with two NQR lines of uncertain relative weights. See the main text for details. Computer-generated data are used. Typical spectral shapes are shown on the left side. (a) Construction of ${\nu }_Q$ as a function of $x_{\text{NQR}}/x_{\text{FSWT}}=w^H$. (b) Linear fits of the two frequency branches. (c) Extraction of $x_{\text{NQR}}/x_{\text{FSWT}}$ knowing ${\nu }_Q$.

Figure 3

Quadrupolar frequency vs $x_{\text{NQR}}/x_{\text{FSWT}}$. The L/${\mathrm{H}}_1/{\mathrm{H}}_2/{\mathrm{H}}_3$ labels refer to the observed frequency branches. Literature data are taken from Refs. [33, 35, 36, 37, 38, 39] (for one sample, the unknown measurement temperature is color coded as white). For $x_{\text{NQR}}/x_{\text{FSWT}}<1,x_{\text{NQR}}$ is determined using the NQR spectral weights (see text for comments about some samples from Ref. [33]). Linear fits are indicated as full lines with attached labels. For each sample, the error on $x_{\text{NQR}}$ is derived from fits of the spectra at one or more temperatures. For $x_{\text{NQR}}/x_{\text{FSWT}}>1,x_{\text{NQR}}$ is determined from the linear extrapolation of the low $x_{\text{NQR}}$ behavior, indicated as a dashed line (when multiple measurement temperatures are available for a single sample, the small variations of ${\nu }_Q$ are accounted for by the horizontal error bars intercepting the dashed line). For each sample, the error on $x_{\text{NQR}}$ is set so as to account for the uncertainty on ${\nu }_Q$, whether experimental on a single point or due to remaining temperature dependence.

Figure 4

Phase diagram of $R{\mathrm{FeAsO}}_{1-x}{\mathrm{F}}_x$ ($R=\text{La}$, Ce, Sm) as a function of $x_{\text{NQR}}/x_{\text{FSWT}}$. For some samples and some transitions, more than one point may be displayed due to characterization using multiple techniques. The samples from the literature are referenced in Table 1, except the undoped Ce-based sample from Ref. [29]. The broad lines are visual guides.

Figure 5

Temperature sensitivity of the quadrupolar frequency, as a function of the peak position at room temperature. $\mathrm{\Delta }{\nu }_Q/\mathrm{\Delta }T$ is calculated from measurements at room temperature and at $T=150$–160 K. The legend indicates $x_{\text{NQR}}/x_{\text{FSWT}}$. For $x_{\text{NQR}}<x_{\text{FSWT}}$, each dotted box groups the points belonging to the same frequency branch (L, ${\mathrm{H}}_1,{\mathrm{H}}_2,{\mathrm{H}}_3$) as defined in Fig. 3. For La-based samples, the hatched rectangle about ${\nu }_Q\approx 11.2$ MHz indicates the frequency range over which $\mathrm{\Delta }{\nu }_Q/\mathrm{\Delta }T$ goes from weak $\left(x_{\text{NQR}}/x_{\text{FSWT}}=1.19\right)$ to zero or negative $\left(x_{\text{NQR}}/x_{\text{FSWT}}=1.90\right)$. Error bars for the Sm-based samples are not shown, as they exceed the actual point dispersion for each frequency branch, suggesting overestimation due to more complex spectra.

Figure 6

Order parameter of the structural phase transition $\epsilon =(a-b)/(a+b)$ ($a,b$: in-plane lattice parameters) as a function of doping. The structural data for all samples are taken from Refs. [29, 49, 50, 51, 52, 53, 54]. The full line is a linear fit, with the dotted line showing its extrapolation to $\epsilon =0$. Vertical dashed lines indicate the percolation thresholds for two- and three-dimensional (2D, 3D) nearest-neighbor square-lattice site percolation.

Figure 7

Uemura plot showing the critical temperature vs ${\lambda }_{ab}^{-2}$. All measured data are taken from Refs. [22, 29, 80] (including one sample whose $x_{\text{NQR}}/x_{\text{FSWT}}$ is determined from its $T_c$ value; see Appendix pp1). $x_{\text{NQR}}/x_{\text{FSWT}}$ is shown as a label. The uncertainty on ${\lambda }_{ab}^{-2}$ is given for all samples where uncertainties on ${\lambda }_{ab}$ and $x_{\text{NQR}}$ are both available. The dashed line is a visual guide. Dotted lines indicate the behavior observed for hole-doped and electron-doped cuprates below or at optimal doping [81, 82]. “s-M” refers to the presence of strong static magnetism, and “SC1+SC2” to the crossover between two superconducting states.

Figure 8

Summary of the interplay of ground states in the doping range where LD-like (blue) and HD-like (red) regions coexist at the nanoscale. The LD-like regions can feature strong (“s-M”) or weak (“w-M”) static magnetism, as well as superconductivity through proximity (“p-SC”). The HD-like regions feature intrinsic superconductivity (“i-SC”), which can be suppressed (“i-SC: lost”). $V_{\text{SC}}$ is the superconducting volume fraction, while “LRO” and “PT” stand for “long-range ordered” and “percolation threshold.” For the magnetic rare-earth case, the intermediate doping region $\left(0<V_{\text{SC}}\le 100\%\right)$ is simplified by not making a distinction between strong static magnetism preventing superconductivity by proximity and destroying nearby intrinsic superconductivity, and by not detailing the behavior close to the 3D percolation threshold, where all of the static magnetism is expected to be weak enough for $V_{\text{SC}}\approx 100\%$.

Figure 9

Phase diagram as used for the determination of $x_{\text{NQR}}/x_{\text{FSWT}}$ for samples from the literature, whose phase-transition temperatures are known but for which no NQR data are available (open symbols). These samples are listed in Table 2. The closed symbols correspond to the samples used to determine the phase diagram (see also Fig. 4).