A structural study of the hole-doped superconductors Pr1−xSrxFeAsO

The structural details of the Pr1−xSrxFeAsO (1111) superconducting system are analyzed using data obtained from synchrotron x-ray diffraction and the structural parameters are carefully studied as the system moves from non-superconducting to hole-doped superconducting with an increase of the Sr concentration. Superconductivity emerges when the Sr doping amount reaches 0.221. The linear increase of the lattice constants proves that Sr is successfully introduced into the system, and the Sr concentration can be accurately determined by electron density analyses. The evolution of structural parameters with Sr concentration in Pr1−xSrxFeAsO and comparison of them to other similar structural parameters of the related Fe-based superconductors suggest that the interlayer space between the conducting As–Fe–As layer and the insulating Pr–O–Pr layer is important for improving Tc in hole-doped (1111) superconductors, which seems to be a different trend from that encountered in the electron-doped systems.


Experimental
Pr 1−x Sr x FeAsO samples with nominal Sr doping amount x from 0.10 to 0.30 were successfully synthesized by using a two-step solid-state reaction method. Firstly, PrAs and SrAs precursors were obtained by making Pr chips (purity 99.95%) and Sr chips (purity 99.5%) react with As powder (purity 99.99%) in the ratio 1 : 1. The mixtures were ground and pressed into pellets. Then, they were sealed in evacuated quartz tubes, followed by heating at 700 • C for 10 h. Secondly, the precursors were smashed and ground together with Fe powder (purity 99.99%) and Fe 2 O 3 powder (purity 99.99%) in stoichiometry as per the formula Pr 1−x Sr x FeAsO. These samples were pressed into pellets and sealed in evacuated quartz tubes and heated at about 940 • C for 5 h, followed by annealing at 1150 • C for 48 h. Then it was slowly cooled down to room temperature.
Synchrotron powder x-ray diffraction (XRD) experiments were performed on a large Debye-Scherrer camera installed at SPring-8 beam line BL02B2 by using an imaging plate as the detector. The wavelength of the x-ray was determined to be 0.602 61 Å by using CeO 2 as the reference. Glass capillaries with an inner diameter of 0.3 mm were used to hold the powder samples in order to eliminate the preferred orientation. The Rietveld refinements were carried out using GSAS in the angle range of 2-70 • with an increment of 0.01 • [20].
Resistivity was measured by employing a standard four-probe method using silver paste for contact. Measurements were carried out with a Quantum Design Physical Property Measurement System (PPMS). dc magnetic susceptibility measurements were performed in a Quantum Design superconducting quantum interference device (MPMS-XL).

Results
Pr 1−x Sr x FeAsO (x = 0.1-0.3) polycrystalline samples with high purity were successfully synthesized using the two-step method mentioned above. We used the high-resolution synchrotron facility at SPring-8 to study the structural details of these samples. The Rietveld refinement results are listed in table 1, and a typical refinement pattern is shown in figure 1. All these samples adopt the tetragonal symmetry with the space group of P4/nmm (129) at room temperature. Some samples have a small amount of Pr 2 O 3 and FeAs as impurities, which hinder the decrease of R p and R wp . The structure of Pr 1−x Sr x FeAsO consists of interleaved twodimensional FeAs and (Pr, Sr)O layers, as shown in the inset of figure 1. The FeAs layer is a conducting layer with Fe in fourfold coordination forming a FeAs 4 tetrahedron, whereas the (Pr, Sr)O layer is insulating and providing charge carriers to the conducting layer. Pr atoms are coordinated with four O atoms in the (Pr, Sr)O layer and are also weakly bonded with four As atoms in the neighboring FeAs layer. In the (Pr, Sr)O layer, Pr is positively trivalent (Pr 3+ ) and O is negatively divalent (O 2− ); the counterpart FeAs layer is negatively monovalent with positively divalent Fe (Fe 2+ ) and negatively trivalent As (As 3− ). The substitution of Pr 3+ with Sr 2+ causes the (Pr/Sr) site positive (3 − δ) charges and, accordingly, the Fe site positive (2 + δ) charge. The charge carriers are transferred through the Pr/Sr plane and the FeAs layer as indicated in figure 1. This suggests that the effect of Sr doping is to facilitate hole transfer to induce hole-doped superconductivity.
We first checked how much Sr was introduced into the structure. In all the samples with nominal compositions of Pr 1−x Sr x FeAsO (x = 0.1-0.3), the Sr atom occupies the same atomic position (2c) as Pr with a certain amount of occupancy, which is precisely determined by the electron density analysis at this site. The results show that the actual doping concentration varies from 0.157 to 0.314. These values deviate from the nominal compositions, but the increasing trend is basically the same. The actual doping concentration is used for the subsequent structural analyses. The atomic occupancies of Fe, As and O were confirmed to be nearly 100%. Given the situation that the ionic radius of Sr 2+ (1.18 Å) is much larger than that of Pr 3+ (0.99 Å) [21], it is reasonable to see a remarkable increase of the lattice constants with an increase of Sr doping concentration. Actually, both a and c increase linearly with x as shown in figure 2, where x is the real doped Sr amount ranging from 0 to 0.314. The data for x = 0 were taken from the previous report [22]. The increase in a is about 0.01 Å (increasing ratio = 0.25%), and the c-axis increases more obviously with 0.06 Å (increasing ratio = 0.7%) with this doping. Consequently, the unit cell volume evolves with Sr concentration in a linear relationship V = 136.411 + 4.217x, which proves the actual introduction of Sr into the structure. In order to study the structure change influenced by doping, we carried out Rietveld refinements in detail based on the synchrotron x-ray powder diffraction patterns. The refinement results are listed in table 1. Figure 4     In the As-Fe-As block, one could see small changes in the Fe-As bond distance and the two Fe-As-Fe bond angles. The Fe-As bond distance increases monotonically up to 0.005 Å with x. Meanwhile, the decrease of the two Fe-As-Fe bond angles is about 0.08 • and 0.04 • . Accordingly, the changes in the bond distance and angles synergistically expand the As-Fe-As block distance from 2.667 to 2.673 Å. It should be noted that this expansion is less than half of the change observed in the Pr-O-Pr block, which results in a remarkable increase of the interlayer distance.

Discussions
Some relatively large Sr 2+ (1.18 Å) substitute for the smaller Pr 3+ (0.99 Å) at the same atomic site, thereby causing the expansion of the unit cell, which was confirmed by x-ray analyses as shown in table 1 and figure 2. The unit cell shows a linear expansion and obeys Vergaard's law, giving further experimental evidence that a replacement of Pr by Sr takes place. Moreover, the introduction of Sr modifies the crystal structure in a delicate way as summarized in figure 4. The Pr-O and Fe-As bond distances increase slightly with x; nevertheless, the values are still comparable with other related compounds. The two Fe-As-Fe bond angles decrease with x, slowly moving toward the ideal values of the perfect FeAs 4 tetrahedron. The evolution of T c as a function of M-Pn-M bond angle is illustrated in figure 7(c) together with those reported for the electron-doped systems [13]. As was admitted in the case of electron-doped pnictide systems, the regular angle of the MPn 4 (M = Fe or Ni; Pn = As or P) tetrahedron is crucial for enhancement of T c . The rich crystallographic information so far available for electron-doped systems shows a clear tendency that the highest T c is achieved at the nearly perfect MPn 4 tetrahedral point. In contrast, only three sets of detailed structural parameters are available for hole-doped systems, i.e. Nd 1−x Sr x FeAsO [17], Ba 1−x K x FeAsO [6] and Pr 1−x Sr x FeAsO (in the present work). Although one can see a similar tendency for hole-doped systems as well, i.e. the regular angle of the FeAs 4 tetrahedron helps enhance T c , nevertheless the T c values are always much smaller than those in electron-doped systems. This phenomenon implies that the Fe-As-Fe bond angle should not be regarded as the only parameter important for tuning superconductivity in hole-doped systems.
In contrast to the slight changes in the Pr-O and Fe-As bond distances as well as the Fe-As-Fe bond angles, the Sr doping greatly changes the two O-Pr-O bond angles and results in the shrinkage of the Pr-O-Pr block. As a consequence, the Pr-As bond distance is largely increased as shown in figure 5. The Pr-As distance increases greatly with x and reaches a maximum of 0.034 Å compared with the parent PrFeAsO [22]. The Pr-As bond distance can give a measure of the interlayer space between the Pr-O-Pr insulating block and the As-Fe-As conducting block. Figure 6 shows the influence of the Pr-As distance on T onset , which was deduced from dρ/dT as given in figure 3(a). In the superconductivity region, T onset increases linearly with the Pr-As distance, indicating that the larger interlayer space favors the improvement of T c . Actually, this feature is observed in the other two hole-doped systems as well. Figure 7(a) shows T c as a function of M-As bond distance in the three hole-doped pnictide superconductors, where M is Ba/K for Ba 1−x K x Fe 2 As 2 , Nd/Sr for Nd 1−x Sr x FeAsO and Pr/Sr for the present system. The M-As bond distances in these compounds are calculated from the reported structural Figure 6. Impact of Pr-As bond distance on T onset . T onset is deduced from dρ/dT as given in figure 3(a). In the superconductivity region, T onset increases linearly with the Pr-As distance, indicating the larger interlayer space favors an improved superconducting transition temperature.
information. Clearly, superconductivity emerges when the interlayer space is expanded to a large extent in all these hole-doped superconductors. The situation can be compared with the different fact that the interlayer space is decreased in several electron-doped (1111) systems. For instance, the Ce-As distance in CeFeAsO 1−x F x decreases linearly from 3.33 to 3.28 Å with x = 0-0.16 [12], which is believed to help bring the Ce(O,F) charge transfer layer closer to the superconducting FeAs one, thereby facilitating electron carrier transfer. Figure 7(b) shows the evolution of T c as a function of the RE-As bond distance in the REFeAsO 1−x F x (RE = Ce) and REFeAsO 1− y (RE = La and Nd) systems [11]- [13]. The observed feature is opposite to the case discussed earlier in the hole-doped systems.
In order to understand the expansion of the interlayer space in the hole-doped systems, the valence state at the Pr site can be considered. We employed the bond valence sum (BVS) theory to evaluate the valence state of Pr [23], where each bond with a distance r contributes to the valence v = exp[(d − r )/0.37] with d being an empirical parameter. Considering the coordination of the Pr site, Pr is bonded with four O atoms in the Pr-O-Pr block and with the other four As atoms in the As-Fe-As block. In the non-superconducting compound with x = 0.157, the four Pr-O bonds are estimated to contribute 2.392 to the Pr-BVS after correction for the Sr doping. The four Pr-As bonds, which are significantly longer, contribute 0.827 to the Pr-BVS. The total Pr-BVS, 3.219, is in good agreement with the expected Pr valence. In the superconducting compound with x = 0.221, the increase in the Pr-O and Pr-As bond distances reduces the Pr-BVS to 2.382 and 0.793, respectively, which gives a total Pr-BVS value of 3.175. These values clearly show that the increase of Pr-As bond distance plays an important role in the reduction of Pr-BVS, and they further confirm that the replacement of Sr decreases the charge at the Pr site. Considering the layer structure of Pr 1−x Sr x FeAsO, Pr/Sr resides at the top and bottom of the Pr-O-Pr block, whereas As resides at the top and bottom of the As-Fe-As block. Therefore Coulombic interactions between the neighboring Pr-O-Pr and As-Fe-As blocks are weakened significantly by Sr doping so that the interlayer space can be expanded.
The expansion of the interlayer space in the hole-doped pnictide systems is reminiscent of the layer-structured metal nitrides, β-MNCl (M = Zr and Hf) [24]. Upon expansion of the interlayer space by the intercalation of Li and tetrahydrofuran in this system, higher transition temperatures are observed. Due to the limitations of the structural information for the holedoped systems at present, we cannot strictly describe how the interlayer expansion favors the (a) T c as a function of M-As bond distance in various holedoped superconductors, where M is Ba/K for Ba 1−x K x Fe 2 As 2 , Nd/Sr for Nd 1−x Sr x FeAsO and Pr/Sr for the present system, respectively. (b) T c as a function of M-As bond distance in various electron-doped systems, where M is Nd for NdFeAsO 1− y , La for LaFeAsO 1− y and Ce for CeFeAsO 1−x F x , respectively. Clearly, superconductivity emerges when the interlayer space is expanded to a large extent in the hole-doped systems. In contrast, the interlayer space is shrunk in the electron-doped systems. (c) T c as a function of the bond angle 1 in various pnictide superconductors. The bond angle 1 was defined as the larger angle between transition metal and pnictide as shown in figure 4(c). Some of these data were taken from [13]. The angle dependence of T c is largely weakened in the hole-doped systems, as compared with the electron-doped systems.
increase of T c in the hole-doped (1111) systems, but the present result will provide the important suggestion that the larger interlayer space between the conducting layer and the carrier-providing insulating layer is one of the key parameters for improving T c in the hole-doped systems.

Conclusion
We successfully synthesized the hole-doped (1111) superconductors Pr 1−x Sr x FeAsO. Superconductivity emerges when x is larger than 0.221 with a large superconducting fraction. Careful comparison between the structural parameters and T c among the various Fe-based superconductors reveals that the interlayer space expands systematically in Pr 1−x Sr x FeAsO with increasing T c . T c reaches its peak when the interlayer space is the largest. This suggests that interlayer space is one of the crucial parameters for achieving higher T c in hole-doped (1111) systems. This is a different trend from that encountered for electron-doped (1111) systems.