Physical properties of superconducting Ca10(Pt4As8)((Fe0.92Pt0.08)2As2)5 crystal and comprehensive cognition on the transition temperature for Ca10-3(4)-8

Superconducting single crystal of Ca10(Pt4As8)((Fe0.92Pt0.08)2As2)5 has been prepared using flux method, and the physical properties of which are careful examined. Resistivity anisotropy between ab plane and c-axis is observed, T −0.5 term originated from the interlayer Josephson coupling is essential to be added to the formula used to describe the out-of-plane resistivity. The density of state (DOS) value at Fermi level derived from the fitting of specific heat data is consistent with the calculation results. Both direct and indirect platinum doping effect have influences on the superconducting transition temperature (Tc) of Ca 10-3(4)-8 system, the Tc of our sample falls well into the trend strip formed by the data reported previously.

Most iron based parent superconductor compounds only exhibit superconductivity upon doping. The reported doping of Ca 10 (Pt n As 8 )(Fe 2 As 2 ) 5 is mainly concentrated in Ca and Fe sites. Nevertheless, changing the replacement rate of Pt for Fe in Ca 10 (Pt 4 As 8 )((Fe 1−x Pt x ) 2 As 2 ) 5 could result in a large range of T c values, for example, T c ∼5.9 K for x=0.07 and T c ∼10 K for x=0.13 under n=3 [2], that means that Pt, as the fundamental component of Pt n As 8 spacer layer, also plays a key role in the substitution within FeAs superconducting layer. On the other hand, even for the same x, there has a large difference in T c between Ca10-3-8 and Ca10-4-8, and the relationship between T c and spacers is complicated, as the spacers change not only interlayer coupling strength, but also act as charge reservoirs, thereby influencing the electronic properties. Empirically, T c correlates with the interlayer distance (d) in a cusp-shaped curvature in both cuprates [13,14] and Fe-based superconductors [15]. However, the Ca 10 (Pt n As 8 )(Fe 2 As 2 ) 5 seems to violate this empirical rule, where T c,max ∼10 K for n=3 with d∼10.5-10.7 Å, and T c,max ∼38 K for n=4 with d∼11.2 Å [1,2]. Given similar d values for both n=3 and n=4, the large difference in T c ought to be attributed to the interlayer spacer: Ca 10 Pt n As 8 . Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Both first-principles calculations and angle resolved photoemission spectroscopy (ARPES) experiments [3,[16][17][18] suggest that Pt n As 8 and FeAs layers are weakly coupled. Through studying the relationship between the structure, constituents and physical properties, the origin of superconductivity for Fe based superconductors may be elucidated. In this contribution, our goal is to synthesize Ca10-4-8 with appropriate Pt doping rate x by controlling the preparation conditions, such as initial element composition, maximum heating temperature and the cooling rate, then measure the physical properties of the samples, through a comparison with the earlier reported data, discuss the reasons for large T c difference in the Ca 10 (Pt n As 8 )(Fe 2 As 2 ) 5 system and seek to an universal interpretation on the transition temperatures in such family.

Sample synthesis and characterization approaches
Synthesis for Ca 10 (Pt 4 As 8 )((Fe 1-x Pt x ) 2 As 2 ) 5 employs a conventional flux method by the process described elsewhere [2,7]. Single crystals preparation starts from mixing of high purity Ca shot (99.999%, Alfa Aesar, Haverhill, MA, USA), Fe powder (99.95%, Alfa Aesar, Haverhill, MA, USA), Pt powder (99.95%, Alfa Aesar, Haverhill, MA, USA), and As powder (99.999%, Alfa Aesar, Haverhill, MA, USA) with a stoichiometric amounts ratio of 13:11:6:23. The mixture was put in a crucible and then sealed in a quartz tube under 1/4 atmospheric pressure of Argon. The whole assembly was heated to 700°C for 5 h within a box furnace and maintained at this Figure 1. Crystal structures of Ca 10 Pt n As 8 (Fe 2 As 2 ) 5 , (a) n=4 and (b) n=3, their cutoff layer (top view) are exhibited below, which show Ca10-3-8 has one less Pt atom than Ca10-4-8 clearly. (c) A prototypical Ca 10 (Pt 4 As 8 )((Fe 1−x Pt x ) 2 As 2 ) 5 single crystals. (d) The diffraction pattern of Ca 10 (Pt 4 As 8 )((Fe 1−x Pt x ) 2 As 2 ) 5 with (00l) peaks. temperature for 4 h. It was further heated up to 1080°C for the next 5 h, and, after being held for 60 h at this maximum heating temperature, it starts to cool. The assembly was firstly cooled to 900°C at a rate of 3°C per hour, and, in the next 50 h, it was further cooled to 600°C. Finally, by turning power off, the furnace was cooled down to the room temperature, and, then, the shiny plate-like single crystals were obtained in the crucible. The cooling process is important to the preparation because it is not only the key factor on the formation of a stable phase, but also has an influence on the diffusion intensity of Pt in the FeAs layer when temperature decreasing, which makes the x changeable. A photo showing the as prepared sample, owning a typical size of 5×4×1 mm 3 , is shown in figure 1(c).
Crystal structure and phase purity were checked by a Rigaku-D/max x-ray diffractometer (XRD), employing Cu-Kα (λ=1.5406 Å) radiation. The surface morphology of the samples was observed by a FEI Quanta 450 scanning electron microscope (SEM) with Oxford EDS detector. The chemical constituent for the sample and Pt self-doping ratio x were determined by Energy Dispersive x-ray Spectroscopy (EDX). Electrical properties and specific heat were measured in a Physical Property Measurement System (PPMS). The standard four-probe method was used for both ab plane and c-axis resistivity measurements. Magnetic susceptibility measurement of the sample was accomplished in a Magnetic Property Measurement System (MPMS).  ( ) at the room temperature, indicative of the sample crystallizing in triclinic space group P1. These parameters are fairly close to those obtained in [1,10].

Results and discussion
The SEM images of the Ca 10 (Pt 4 As 8 )((Fe 1−x Pt x ) 2 As 2 ) 5 single crystal are shown in figure 2(a). As can be seen that the crystal does not only own a surface with large flat and homogeneous area, but also exhibit the layered nature. The chemical constituents were determined by the EDX measurements. We selected five scattered spots on each sample, then calculated the average value of these scan results. The measured composition is Ca 10 Pt 4.8 Fe 9.2 As 18 , implying a formula of Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 for the sample, if platinum selfdoping effect is considered. Compared with the work of x=0.14 [10], besides that the content of Pt in the original mixture was reduced, the cooling time is also shortened, which is not advantageous to the interlayer diffusion of Pt, and this may be other reason for the decrease of the Pt doping level x in the FeAs layer.
Both ab plane r ab ( )and c-axis r c ( ) electrical resistivities of Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 are shown in figure 3. The overall features of ρ ab are consistent with the previous reports [1,2,7]. The r ab values decrease monotonously from 0.375 mΩ•cm at 300K to 0.15 mΩ•cm before superconducting transition in its normal state, exhibiting a metallic character > r ab starts to fall steeply and touch to zero at 28.7 K, implying the transition width in temperature is D = Relatively small RRR and large T _ c onset indicate that there are platinum ions taking the place of iron in the FeAs layers [1][2][3][7][8][9], and the narrow transition process indicates high quality and spatial composition uniformity of grown crystal. By contrast, the behavior of ρ c is different with that of ρ ab , it rises very slowly with descending T at high temperatures between 200 and 300 K and starts to increase with decreasing T rapidly under 150K, manifesting a semiconductor-like behavior < forms a peak at 35 K before dropping to zero resistivity. In the Ca10-4-8 system, this kind of transport anisotropy between ab plane and c axis is regarded as intrinsic.  Owing to the layered structure, the ab plane resistivity for Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 could be described by a shunt resistor connection model. Figure 4(a) displays such a schematic.
The value of net resistance (R) follows the formula below: where n, R Ca , R Pt4As8 and R FeAs are the number of FeAs-Ca-Pt 4 As 8 -Ca layers, the resistance of the Ca layer, Pt 4 As 8 layer and FeAs layer, respectively. In a parallel configuration, the current always seeks to the path with the minimum resistance to flow, and deviates from any obstruction. Here, Ca layer could be treated as insulating and the value of R Ca tends to infinity, while the FeAs and Pt 4 As 8 layers contribute the most of electronic states to the Fermi level, and they carry the majority of the electric current. Thus, only the first two items in formula (1) need to be considered, and the representation of ρ ab -T curve in the normal state, whether on shape or magnitude, is jointly dominated by the conductive properties of FeAs and Pt 4 As 8 layers.
The ab plane resistivity data r ab ( 50 K<T<300 K) could be fitted by r = +´a P Q T , ab the green solid line in figure 3(a) is the fitting curve with =  W P 0.041 0.0008m cm, · =  W Q 0.022 0.002m cm K 0.482 · ·and α=0.482, all reported ρ ab for Ca10-4-8 has the similar dependence on temperature (∼T 0.5 ) [1,2,7]. In degenerate semiconductors and disordered metals, this kind of dependence originates from the charge carrier scattering by impurities [19,20], and structural studies for Ca10-4-8 reveals the existence of partial replacement of Fe by Pt within the (Fe 1-x Pt x ) 2 As 2 layer and possible Pt deficiency in the Pt 4−δ As 8 layer [3,8,16,17]. Thus, the carriers in both (Fe 1-x Pt x ) 2 As 2 and Pt 4−δ As 8 layers could be affected by the crystallographic disorder, which may account for the quasi square-root temperature dependence of ρ ab in Ca10-4-8 system.
When discussing the resistivity along the c direction, we can write the value of net resistence (R) as: R=n (R FeAs +R Pt4As8 +2R Ca ), and the schematic plot exhibits in figure 4(b). The c-axis resistivity r c ( 70 K<T<300 K) could be fitted by 60.093 1.846 m cm K . 1 2 · · / The quasi square-root temperature dependent term Q′×T 0.482 in ρ c originates from the in-plane scattering, which could be attributed to the crystallographic stacking fault [2], the value of index 0.482 is derived from the fitting results of ρ ab . Since the spacer layer Ca-Pt 4 As 8 -Ca should be treated as insulating, intrinsic Josephson junctions (iJJs) are shaped along the c direction of Ca10-4-8 crystal by alternative stacking of the FeAs superconducting layer and Ca-Pt 4 As 8 -Ca insulating layer, that's the reason why normal state r c is much larger than r ab as shown in figure 3, therefore, the S′/T 0.5 component in ρ c is proposed in reference [21] to describe the resistivity of this kind of interlayer incoherent scattering. The value of Q' is far smaller than that of S', indicating the Josephson tunneling effect is dominant in the ρ c , the influence from both in-plane scattering and crystal defect are relatively little. Figure 5 displays the resistivity anisotropy calculated by. The value of γ at room temperature 300K is slightly bigger than 4, with the temperature decreasing, γ increases gradually, reaching to ∼9 around T c , which is larger than that of LaO 1−x F x FeAs [22], the most anisotropic system among traditional Fe based superconductors. The value is also larger than that of the work γ∼8 at T c ∼34 K with x=0.14 [10]. It appears that for Ca10-4-8, the smaller Pt doping level x, the lower T c and a much more anisotropic system acquires.    if T c_onset is taken as 31.6K. Because of the existence of strong thermal vortices fluctuations in the system, the phenomenon of ΔT c widening with rising applied field is only observed in the copper based superconducting materials previously [23]. By contrast, in the case of current flowing along c-axis and applied field parallel to the ab plane of the sample, both T c_zero and T c_onset shift to lower temperatures synchronously, as shown in figure 6(b). Therefore, ΔT c seems unchanged with the increasing applied field, and ΔT c under such condition is also far smaller than that in the case of I//ab and H//c shown in figure 6(a).
The variation of the upper critical field H c2 (T) with temperature for Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 is shown in figure 7. The values of H c2 (T) are determined as the field at the 90%, 50% and 10% of the normal resistivity ρ n before superconducting resistive drop, which is indicated by dot lines in figure 6.
The   The superconducting magnetic susceptibility of Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 is shown in figure 9(a). Under a low applied field of 20Oe, the zero field cooling (ZFC) curve starts to exhibit a diamagnetic signal at 31.2K, which is in agreement with our resistivity analysis given in figure 3. Below 15K, the full diamagnetism appears, indicative of bulk superconductivity in the sample.
Normal state susceptibility χ measured at relatively high magnetic field 0.1Tesla is observed in figure 9(b). An anomaly could be found at around 75K for both ZFC and FC measurements. Above 75K, the susceptibility does not only decrease with decreasing temperature, but exhibits a quasi-linear T dependence in a wide temperature range, the black solid line is the fitting for χ in figure 9(b). This kind of unusual paramagnetic state is also existed in other Fe based superconductors or compounds, such as the 1111, 122 and 11 family [25][26][27][28][29], and the theoretical investigations have shown that it may originate from the strong (π, π) short-range antiferromagnetic (AFM) spin fluctuation in the system [30,31]. Below 75 K, χ starts to increase as temperature decreases, and this upturn could also be found in previous reports on Ca10-3(4)-8 system [2,32]. Considering its order of magnitude (∼10 -3 ) as well as the fact that χ manifests no saturation at low temperature region, this upturn acts more like the 'Curie tail' phenomenon rather than an influence from the ferromagnetic impurities inside the sample. Figure 10(a) presents the temperature dependent C p (T)/T data, where C p (T) is the specific heat of Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 and T is the temperature. As it can be seen, an apparent slope change happens at 31.2 K, confirming the bulk superconducting transition of our sample, which is fully consistent with the observation in the resistivity and susceptibility measurements. Figure 10(b) shows the tail of the C p (T) curve in the temperature range between 2 and 4 K under the magnetic fields H=0 and 5 T for Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 with H⊥ab, the inset displays its corresponding C p (T)/T versus T 2 plots. Below 4 K, assuming no magnetic excitation exists, C p (T)/T should follow the relation of where γ is the electronic specific heat coefficient and β reflects the contribution from phonon to C p (T). Fitting results listed in table 2 show that the magnetic field has nearly no impact on the values of β, but affects γ significantly. This is because that H could kill Cooper pairs in the superconducting state and release more free electrons to the system, and then increases γ and enhances the electrons specific heat conspicuously.
The density of states (DOS) at the Fermi level for both spin directions N(E F ) could be estimated by γ using the following relation [33],  where =´k JK 1.38 10 B 23 / is the Boltzmann constant and λ ep is the electron-phonon coupling constant. In the first approximation, λ ep =0 can be adopted, which gives N(E F )= 31.2 and 44.7 states /(eV·f.u.) at H=0 T and 5 T, individually. These results are also listed in table 2. The value of N(E F ) at H=0 T is close to but a little larger than that of the reported in [16] ∼28.54 states/(eV·f.u.) and our calculation result ∼29.87 states/(eV·f.u.) shown below. The fact that λ ep could be set to zero illustrates unlike the traditional superconductors which mainly depend on the help of strong interactions between electrons and phonons to form Cooper pairs, for example λ ep =1.6 3 for Hg and λ ep =1.8 35 for Nb 3 Sn [34], the electron-phonon coupling is relatively weak in the Fe based superconductors. From the value of β, the Debye temperature Θ D of the crystal can be evaluated using the expression [33], is the universal gas constant, N is the number of atoms per formula unit. The values for β yield Θ D =198.38(7) K and 197.19(9) K under H=0 T and 5 T, separately, which are listed in table 2 together.
The value of DOS derived from the specific heat data is consistent with our calculation results mapped out in figure 11.
As can be seen from figure 11, after transferring all its conductive electrons to the Pt 4 As 8 and FeAs layers, the Ca sheet nearly gives no contribution to the DOS around Fermi level (E F ), which should be regarded as insulate as we treated in the resistivity analysis. For Ca10-3-8 and Ca10-4-8, the Fe-3d PDOS are similar, the Fermi levels all locate at the hillside of their Fe-3d peaks, confirming that iron contributes the majority of electronic states near Fermi level in both compounds, and conduction for the two compounds is expected to be anisotropic. With regard to Pt n As 8 layer, the Pt-5d PDOS forms a quasi-gap around the Fermi level, indicating the contribution of  Solid round dot, asterisk, triangle, diamond, square, empty round dot, cross, empty triangle and inverted triangle reflect T c from [1][2][3][7][8][9][10][11][12], respectively, multiple sign represents this work. Same symbol is from the same bibliography, the color of red is for Ca10-3-8 and blue is for Ca10-4-8. Dot lines are guided for eye to show T c saturation with increasing x for Ca10-3-8.
Pt n As 8 layer to DOS at E F to be relatively small. However, things are not exactly the same even for those two compounds, the Fermi level almost crosses the gap in the Ca10-3-8 phase, but is pushed up slightly above this gap for Ca10-4-8. This does not only make the Pt 4 As 8 layer to be semi-metalic, but also lead to the band filling for Ca10-4-8 around the gap in Pt states mainly fills the Fe states, which is equivalent to an indirect electron doping from Pt 4 As 8 layer to the FeAs layer.
As can be seen in figure 12(a), the points are clearly divided into two sets, those for Ca10-3-8 with relatively smaller T c flock together at the left lower corner, while the points with higher T c on the top half of the graph all belong to Ca10-4-8, which increase with increasing x. In other words, even with the same platinum contents, the superconducting transition temperature for Ca10-4-8 is far larger than that for Ca10-3-8. We know that the FeAs layer serves as the superconducting layer in the Fe based superconductors, and, then, any excessive change or deterioration of which will greatly reduce the transition temperature. Compared with Ca10-4-8 containing the same amount of platinum, Ca10-3-8 have one less Pt atom in its PtAs layer and it means that much more Pt atoms will enter FeAs layer, some of them replace the Fe atoms and others may be the interstitial acting as the scattering centers, which add lattice disorder and lead to the free carriers localization within the system [35].
Similar cases also occur in other directly Fe substituted compounds, for example, a maximum T c of 16.5 K is achieved at x≈0.29 for isovalent doped Ba(Fe 1−x Ru x ) 2 As 2 [36], even for the electron-doped Ba(Fe 1−x RE x ) 2 As 2 (RE=Co, Rh) [37,38] with maximum T c values are around 24 K. However, the same electron-doped SmFeAsO 1−x F x , which leaves the FeAs layer untouched, have T c as high as 55 K [39], more than double the former. Thus, it can be concluded that under the precondition of same total Pt concentration, the accumulation of redundant Pt 2+ in FeAs layer is the main reason that limits T c of Ca10-3-8.
To understand the influences of doping level for Ca 10 (Pt n−δ As 8 )((Fe 1−x Pt x ) 2 As 2 ) 5 on the transition temperature in detail, the relationship of T c versus x available in previous reports is plotted in figure 12(b).
In ReFe 2 As 2 (Re=Ba, Sr) system, despite the isovalent, a certain amount of non-magnetic Pt 2+ ions replacing the Fe 2+ would disturb the AFM order in the FeAs layer, and it suppresses the spin density wave (SDW) transformation and induces superconductivity. In such condition, the typical features are, first, T c is rarely beyond the limits of 25K, and the reason has been stated above. Second, in a certain doping range, T c increases with increasing x and eventually reaches saturation. Third, only when the doping level reach a certain value, for example x>0.02, superconductivity emerges [40][41][42]. It is found that the relation of T c with x of Ca10-3-8, as shown in figure 12(b), meets these three points accurately, indicating that Ca10-3-8 and Re(Fe 2−x Pt x ) 2 As 2 (Re=Ba, Sr) type compounds may share the very similar even the same superconducting mechanism, and the n=3 compound with x=0 could be regarded as the parent of this family of superconductors.
With regard to Ca10-4-8, things turn wholly different. Compared with Ca10-3-8, an extra Pt atom on the Pt 4 As 8 layer makes Ca10-4-8 exceed the Zintl-Klemm concept (ZKC), leading to a configuration of + + + -+ -e Ca Fe As Pt As 2 . The two unbound electrons push the Fermi surface of Ca10-4-8 higher than its Pt-5d energy gap, this realizes the indirect electron-doping to the FeAs layer, which greatly increases T c values for Ca10-4-8. That is the reason why even if x∼0, Ca10-4-8 could gain such a higher T c as 30 K, which is also same as the case that La replaces the Ca in Ca10-3-8 and raises its T c up to ∼30K [4,8,11,32]. Generally, in the Ca10-4-8 system, Pt element has both direct and indirect doping of FeAs layer, the indirect doping enhances T c conspicuously, and the direct makes T c increase with increasing x almost linearly in a certain doping range. Under the combined effects, the reported T c s form and distribute into a quasi-linear strip in the upper part of figure 12(b).

Conclusions
To summarize, Pt doping level x in the FeAs layer can be adjusted, within a certain degree for Ca10-4-8, by controlling the initial element portion and the cooling rate during the heating stage in the synthesis process. XRD, EDX, resistivity, magnetoresistance, magnetic susceptibility and specific heat were measured on the high quality Ca 10 (Pt 4 As 8 )((Fe 0.92 Pt 0.08 ) 2 As 2 ) 5 single crystal. The anisotropic property between ab plane and c-axis resistivity is observed, a T α (α∼0.5) type of temperature dependence for the normal state ab plane resistivity should be the consequence of disorder, and S′/T 0.5 term originating from Josephson coupling is needed to add to the formula that describes the c-axis resistivity, which is intrinsic to Ca10-4-8. The H c2 and ξ parameters were obtained through the magnetoresistance in the superconducting state, and H c2 was relatively large for our sample. The DOS at Fermi level was estimated by specific heat and it was comparable to the calculated results.
Both direct and indirect Pt doping effects on FeAs layer push transition temperature of Ca10-4-8 over 30 K, and T c of sample with x=0.08 falls well into the trend strip formed by the collective data reported previously.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.