Phase Diagram and Weak-link Behavior in Nd-doped CaFe_2As_2

The transport properties, phase diagram, and dopant distribution are investigated in systematically Nd doped CaFe_2As_2 single crystals. Coexistence of two superconducting (SC) phases with different critical transition temperature (T_c) is observed. The low-T_c phase emerges as x>= 0.031, and the T_c value increases to its maximum value of about 20 K at x = 0.083, the maximum doping level in our study. As x>= 0.060, the high-T_c phase with a T_c value of about 40 K is observed. The structure transition (STr) from tetragonal to orthorhombic phase vanishes suddenly around x = 0.060, where a new STr from tetragonal to collapsed tetragonal phase begins to turn up. Compared to the low-T_c phase, the end point of SC transition of the high-T_c phase is more sensitive to the magnetic field, showing a characteristic of Josephson weak-link behavior. Possible scenarios about this system are discussed based on our observations. We also find that the non-uniform SC properties cannot be attributed to the heterogeneous Nd distribution on the micro scale, as revealed by the detailed energy dispersive X-ray spectroscopy (EDS) measurements.


Introduction
Fe-based superconductors have been studied extensively since the report of LaFeAsO 1-x F x with T c of 26 K [1,2]. Among the different systems, the AFe 2 As 2 compounds (A=Ba, Sr, Ca, Eu, so called "122" system) with the ThCr 2 Si 2 -type structure [3] are widely studied because single crystals with high quality are easily accessible [4]. The parent compounds of the 122 system undergo a phase transition from a high temperature tetragonal, paramagnetic phase (T phase) to a low temperature orthorhombic, antiferromagnetic phase (O phase). The antiferromagnetic order can be systematically suppressed and superconductivity can develop by the means of chemical substitution or applying pressure. The highest T c value in the 122 system is still lower than 55 K in the RFeAsO (1111) system [5]. Superconductivity with maximum T c of 38 K has been achieved in the Ba 1-x K x Fe 2 As 2 by hole-doping [6].
Meanwhile, electron-doping usually induces superconductivity at a lower temperature (around 22 K) by substituting Fe ions with other transition metals [7][8][9]. This is typically attributed to the imperfection of the FeAs conducting layer induced by doping.
In order to further enhance the T c , much attention has been paid to electron doping approached by substitution of trivalent rare-earth elements ions (Re 3+ ) on divalent A 2+ ions in 122 system without affecting the FeAs layers [10][11][12][13][14][15][16]. However, superconductivity in single-crystalline samples is only attained in systems based on CaFe 2 As 2 . Besides the T-O transition at ambient pressure for CaFe 2 As 2 , the tetragonal phase transforms to a new collapsed tetragonal structure (cT, both the a-axis and c-axis lattice shrink) when a hydrostatic pressure (> 0.35 GPa) is applied [17,18].
Recently, it is found that this cT phase can be stabilized at ambient pressures by doping Pr or Nd into CaFe 2 As 2 . In contrast, the substitution of up to 28% La or 17% Ce does not drive this T-cT transition [12]. More surprisingly, two superconducting phases with T c of about 20 K and 40-49 K respectively were discovered in the rare-earth doped Ca 1-x Re x Fe 2 As 2 (Re = La, Ce, Pr, Nd) compounds, regardless of this T-cT structural evolution [12][13][14][15][16]. Although the high-T c phase exceeds the highest T c ~ 38 K in the hole-doped Ba 1-x K x Fe 2 As 2 , the superconducting volume fraction is very 3 low suggesting the absence of bulk superconductivity. The origin of the non-bulk and two-phase superconductivity has be attributed to the minor foreign phase, interface or filamentary superconductivity, Josephson junction coupling between grains et al, which is still an open issue and needs more in-depth investigations [14,19,20].
To the best of our knowledge, a systematic investigation on the Nd-doped CaFe 2 As 2 system is still lacking. Moreover, the temperature versus doping phase diagram of this system is still not clear. In the present work, we report a systematic investigation of the characterization and phase diagram of the electron-doped Ca 1-x Nd x Fe 2 As 2 single crystals. The behaviors of field induced resistance broadening for superconducting transition are also observed, indicating a weak-link feature in the present system.

Experimental Details
Single crystals of systematically Nd-doped CaFe 2 As 2 were grown using a self-flux method. The The phase identification and crystal structure were characterized by X-ray diffraction (XRD) with Cu K radiation. The actual Nd concentrations were checked and determined by the energy dispersive X-ray spectroscopy (EDS) measurements.
The resistance measurements with magnetic fields up to 9 T were carried out by using a standard four-contact method with a quantum design physical property measurement system (PPMS). Figure 1a shows the XRD θ-2θ patterns for four typical Ca 1-x Nd x Fe 2 As 2 single 4 crystals with different doping levels. The sharp (00l) diffraction peaks suggest that the crystallographic c-axis is perpendicular to the plane of the single crystals with an excellent crystalline quality. The calculated c-axis lattice parameters as a function of Nd content are plotted in Figure 1b. The data of parent phase are taken from the report by S. R. Saha et al. [12]. It can be found that c axis shrinks monotonously with increasing x, which implies a successful chemical substitution and is also consistent with previous reports [12]. for eyes. The data of parent phase are taken from the report by another group [12]. Figure 2 presents the temperature dependence of resistivity under zero fields for Ca 1-x Nd x Fe 2 As 2 single crystals, normalized to the data at 300 K. The data of parent phase are taken from the report by another group [12]. Several features are observed at different temperatures. In the inset of figure 2, we denote them by arrows for the sample with x = 0.060 as an example, where T O , T cT , T cH , and T cL represent the transition temperature to the orthorhombic phase, to the collapsed tetragonal phase, the onset transition temperature of high-T c phase, and that of the low-T c phase, respectively. Figure. 2. Temperature dependence of the in-plane electrical resistivity for Ca 1-x Nd x Fe 2 As 2 single crystals, normalized to the data at 300K. The data of parent phase are taken from the report by another group [12].

Results and discussion
From our data we can see that with Nd doping the resistivity anomaly due to the tetragonal to orthorhombic STr shifts gradually to lower temperature and disappears around x = 0.060. Another conspicuous feature is a sharp and dramatic drop in resistivity when the doping level x ≥ 0.060. This feature is associated with a STr from T phase to cT phase [12,17]. We note that there exists a hysteresis for the T-cT STr with increasing and decreasing the temperature. Here we only show the data collected with increasing the temperature. With increasing x, this resistivity transition shifts to higher temperatures, which is similar to that observed in Ca 1-x Pr x Fe 2 As 2 based on neutron-diffraction measurements [12]. For the sample with x = 0.060, the coexistence of two structure transitions may be due to the local inhomogeneity. Along with the suppression of T-O phase transition, resistivity decreases quickly below 10 K 6 as x ≥ 0.031, suggesting the appearance of a superconducting transition. When x ≥ 0.060, two superconducting transition steps appear in low temperature region, which seems to be a common feature in Ca 1-x Re x Fe 2 As 2 . Both superconducting transitions are broad and no zero resistance was observed in some of the samples down to 2 K. Figure. 3. Doping-temperature (x-T) phase diagram of Ca 1-x Nd x Fe 2 As 2 . The data of parent phase are taken from the report by another group [12]. The regions with different colors represent the different structural phases. The two SC phases with different T c are revealed by black and blue patterns, respectively.
Based on the resistivity behavior described above, we can establish a doping-temperature (x -T) phase diagram for Ca 1-x Nd x Fe 2 As 2 , which is shown in figure 3. In the lower-doped side (x ≤ 0.060), superconductivity of low-T c phase coexists with T-O transition. Similar behaviors have also been observed in the hole-doped Ba 1-x K x Fe 2 As 2 [21], electron-doped BaFe 2-x Co x As 2 [22] and other rare-earth doped CaFe 2 As 2 systems [13]. When the doping level increases to 0.060, To check the influence of magnetic fields on the two superconducting phases, we measured the temperature dependence of the resistivity under different magnetic fields up to 9 T. The magnetic fields were applied along the c-axis of the single crystals. Here we show the data for one sample with x = 0.060 (denoted as 0.060-2) in figure 4. The transition temperature of superconductivity is suppressed gradually and the transition is broadened with increasing the magnetic fields. However, obvious differences for the influence of magnetic field on the two SC phases are observed. An unconspicuous field induced resistance broadening behavior is observed in the low-T c phase. For the high-T c phase, in contrast, the end point of the SC transition is very sensitive to the magnetic field, which shifts obviously to lower temperatures even under a magnetic field of 0.05 T. We argue that this is a typical characteristic of Josephson weak links, which has been observed at the high-angle grain boundaries in high-T c cuprate superconductors [24,25].
We attempted to further explore the possible origins of the non-uniform SC properties in the present system. The distribution of the Nd-dopant on micro-scale is is similar to that reported on Pr-doped CaFe2As2 system [20]. The full width at half maximum (FWHM) of the profile for the histogram in figure 5(b) is about 0.009. Our data indicate that the two-SC-phase feature observed in the present system cannot be attributed to the Nd distribution on the micro scale. Of course we cannot rule out possible heterogeneous features responsible for the non-uniform SC behaviors on a 9 smaller scale (e.g. nano scale). It was indicated that the high-T c phase is not an interfacial superconductivity [23] or a filamentary-type superconductivity caused by local pinning strength and local structural defects [12,13]. Very recently, K. Gofryk et al. [20] reported that the inhomogeneous and strongly localized high-T c phase is a kind of granular filamentary superconductivity emerging from clover-like regions associated with Pr dopants composed of 3 or 4 atoms in Pr-doped CaFe 2 As 2 . These regions with a SC gap of Δ ~ 30 meV are separated and surrounded by other low-T c phases with Δ ~ 15 meV and non-SC regions. So the weak-link behavior of high-T c phase observed in our data is likely to originate from the boundaries between these high-T c regions.

Conclusions
In the present work, we have investigated the phase diagram and field induced resistance broadening behavior of Ca 1-x Nd x Fe 2 As 2 single crystals. It is found that