Iron arsenides with three-dimensional FeAs layer networks: Can(n+1)/2(Fe1−xPtx)(2+3n)Ptn(n−1)/2As(n+1)(n+2)/2 (n = 2, 3)

We report the comprehensive studies between synchrotron X-ray diffraction, electrical resistivity and magnetic susceptibility experiments for the iron arsenides Can(n+1)/2(Fe1−xPtx)(2+3n)Ptn(n−1)/2As(n+1)(n+2)/2 for n = 2 and 3. Both structures crystallize in the monoclinic space group P21/m (#11) with three-dimensional FeAs structures. The horizontal FeAs layers are bridged by inclined FeAs planes through edge-sharing FeAs5 square pyramids, resulting in triangular tunneling structures rather than the simple layered structures found in conventional iron arsenides. n = 3 system shows a sign of superconductivity with a small volume fraction. Our first-principles calculations of these systems clearly indicate that the Fermi surfaces originate from strong Fe-3d characters and the three-dimensional nature of the electric structures for both systems, thus offering the playgrounds to study the effects of dimensionality on high Tc superconductivity.

Both copper-and iron-based superconductors share structural low dimensionality, leading to the speculation that reduced dimensionality might be essential for iron-based superconductors as well as copper-oxide superconductors [1][2][3][4] . In fact, enhanced spin fluctuations that arise from reduced dimensionality have been regarded as a crucial factor for the emergence of high T c superconductivity in iron-based systems 3 . On the other hand, some experimental results lead us to question the importance of low dimensionality for some iron-based systems: (i) nearly isotropic nature in underlying electric states 5 , (ii) fairly substantial interlayer magnetic interactions [6][7][8][9][10][11] , and (iii) different dimensionality of the Fermi surfaces between hole-and electron-doped systems [12][13][14][15] . To understand the effects of dimensionality on iron-based superconductors, the exploration of novel iron arsenides without two-dimensional lattice structures has been vigorously pursued 16,17 . Very recently, the emergence of pressure-induced superconductivity was reported in BaFe 2 S 3 with quasi one-dimensional ladders, implying the unnecessarily of the structural two-dimensionality for superconductivity 18 . We expect these studies will provide important insights by comparing their physical properties and electric structures with those in conventional iron-based systems with two-dimensional structures in lattice structures. For example, spin ladders in copper oxides can be used to elucidate the high T c mechanism 19,20 .
In this paper, we report the relationship between crystal structures and physical properties for the iron arsenides with three-dimensional FeAs networks, Ca n(n+1)/2 (Fe 1−x Pt x ) (2+3n) Pt n(n−1)/2 As (n+1)(n+2)/2 with n = 2 and 3, where the horizontal FeAs layers are bridged by inclined FeAs planes through edge-sharing FeAs 5 square pyramids. Although the initial structural study has been already performed by another group 21 , we present the details of the crystal structures of these systems, clarified by synchrotron single-crystal X-ray diffraction experiments. We further exhibit the resistivity and magnetic susceptibility of these systems and show a sign of superconductivity in n = 3 systems with a small volume fraction, indicating local superconductivity in the crystal. Based on the structural parameters collected using synchrotron X-ray diffraction experiments, we clarify the three-dimensional nature in electric structures for these systems by first-principles calculations using the WIEN2k package.

Results
Single-crystal X-ray diffraction experiments revealed that the both systems crystallize in monoclinic structures. Through careful investigation of the extinction rule of k = 2n + 1 for 0k0, we found that the non-centrosymmetric space group P2 1 (#4) or the centrosymmetric space group P2 1 /m (#11) can be realized for both systems. Our structural analysis revealed that reliability factors based on the structural factors remain almost unchanged, regardless of the presence of centrosymmetry. Thus, we determined the space group to be P2 1 /m (#11) with higher symmetry for both systems. The refined conditions and obtained lattice parameters are summarized in Tables S1 and S2, respectively. The refined structures are stable in the temperature range between 42 K and 300 K. The temperature dependence of the lattice parameters for the n = 3 system is presented in Fig. S1.
The obtained crystal structures are shown in Fig. 1a and b for the n = 2 and 3 systems, respectively (see the Supporting Information for crystallographic data). In both systems, α-type is realized, as shown in the previous study 21 . The overall appearance shows triangular tunneling structures rather than the layered structures found in conventional iron-based superconductors because of the presence of FeAs bridges connecting adjacent FeAs layers. By using the single crystal synchrotron X-ray diffraction data collected at SPring-8, we clarified that the platinum substitutions occur at all iron sites composing the FeAs layers and bridges. Further amounts of substitutions occur in FeAs bridges compared with the FeAs layers both for n = 2 and 3 systems, as summarized in Table S2. As shown in Fig. 1c, the FeAs layers and bridges are connected through edge-sharing FeAs 5 square pyramids, where platinum ions are excluded. In the vacant channels enclosed with FeAs planes, apical-sharing PtAs 3 planar triangles and calcium ions are incorporated, as shown in Fig. 1a and b.
Our resistivity measurements show signs of a superconducting transition in the n = 3 system, while the n = 2 system is a normal metal down to 2 K. Due to the whisker-shaped single crystals that grow along the b-direction in relation with the tunneling structures shown in Fig. 1d and e, we can easily measure the temperature dependences of electrical resistivity along the b-directions for both systems. While the n = 2 system shows metallic conductivity without exhibiting any signs of a superconducting transition down to 2 K, the n = 3 systems undergo a drop in resistivity in low temperatures, which is characteristic of a superconducting transition, as presented in Fig. 2a. The onset T c is 30 K, which is almost consistent among the four measured samples (samples A-D); however, the temperature dependences apparently differ depending on samples, as shown in the inset of Fig. 2a. By increasing the magnetic field perpendicular to the b-axis up to 7 T for sample A and B, the superconducting transition is gradually suppressed, as shown in Fig. 2b. The inset of Fig. 2b shows the temperature dependence of the upper critical field H c2 for sample A and B. Here, the transition temperature is determined from the midpoint of the resistive transition. For both samples, H c2 increases almost linearly with decreasing temperature in the 0-7 T range, although the slope differs. Corresponding to the superconducting transition in electrical resistivity, the magnetic susceptibility measurement shows a small diamagnetic signal with a shielding volume fraction (VF) of less than 1% with a small ferromagnetic hysteresis, which probably comes from the impurity phases, such as unreacted iron. Our additional magnetic susceptibility measurements using piston cylinder cell clarified that VF does not increase by applying pressure up to 1.4 GPa (data not shown): VF retains small under applied pressure.
Here, we should focus our attention on the origin of superconductivity with small VF. Although we cannot completely exclude the possibility that the tiny amount of impurities, such as Ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5 with T c = 38 K 22 , show superconductivity, we can safely say that the large amounts of impurity phases are not included in our samples based on the single crystal X-ray diffraction experimental results using the samples A-D, as shown in the Fig. S2. One possible scenario is the trace superconductivity appears in the n = 3 system, as is often found in another iron based compounds 23,24 . In the present systems, fairly amounts of platinum ions are doped to the iron sites, which may introduce the local strain originating from the inhomogeneous distribution of dopants, leading to the trace superconductivity. Considering that the bulk superconductivity often arises by the appropriate substitution 25 , further exploration of these systems may give us opportunities to study the bulk superconductivity.
For further considering the possibility for realizing superconductivity on the three-dimensional network structures, it is worth discussing the regularity of FeAs 4 tetrahedra in the present n = 2 and 3 systems because the intimate relationship between the regularity of FeAs 4 tetrahedra and the superconducting transition temperatures has already been clarified for conventional iron based superconductors with two-dimensional lattice networks 26 . In the present n = 2 and 3 systems, the FeAs planes and bridges are constructed by several crystallographically inequivalent FeAs 4 tetrahedra, resulting in differing regularity depending on the site. As a common feature between the present systems, the FeAs 4 tetrahedra around the FeAs 5 square pyramids are strongly distorted. The As-Fe-As bond angles of α, β and γ with the arsenic ions composed of FeAs 5 square pyramids (Fig. 1c), are much smaller than the angle (109.47°) of the regular tetrahedron; α = 99.774°, β = 102.781°, and γ = 95.253° are realized in the n = 2 system, while α = 102.42°, β = 105.296°, and γ = 93.236° are found in the n = 3 system. The regularity of the FeAs 4 tetrahedra gradually recovers away from the FeAs 5 square pyramids, indicating that the longer distance between neighboring FeAs 5 square pyramids is favorable to superconductivity by increasing the more regular FeAs 4 tetrahedra. Further explorations of homologous compounds with n ≥ 4 may be leading to the bulk superconductivity with three-dimensional structure.
Finally, we would like to present the three-dimensional electric structures for the present systems clarified by the first-principles calculations using the WIEN2k package 27 to investigate the relationship between the electric and lattice structures. For simplification, we performed the calculations for Ca n(n+1)/2 (Fe 1−x Pt x ) (2+3n) Pt n(n−1)/2 As (n+1)(n+2)/2 for n = 2 and 3 without replacing Fe with Pt, although these systems have not been experimentally synthesized. The structural parameters supplied in Table S2 were employed for the calculation. Figure 3a and b show the results of our first-principles calculations. The overall appearances of Fermi surfaces are much more complex than those in other iron-based superconductors. As shown in the insets of Fig. 3a and b, both Fermi surfaces originate from strong Fe-3d characters, without any dominant contributions from other elements such as Ca, As, and Pt, which is a common feature among conventional iron-based superconductors. Further investigation of the partial DOS for each Fe site confirmed that the Fermi surfaces are constructed by the contributions of all iron sites including site 1 at the FeAs 5 square pyramid and sites 2-4 at the strongly distorted FeAs 4 tetrahedra, as shown in Fig. 4a and b. These results clearly indicate the three-dimensional nature of the electric structures with strong Fe-3d characters of the present systems, which should be compared with the two-dimensional nature in the conventional iron-based superconductors.
The electrical dimensionality has been thought to be an essential factor for high T c superconductivity for iron-based superconductors as well as copper-oxide superconductors. The extensive studies have been performed toward the realization of superconductivity with lower dimensionalities in electric structures 16,17 , inspired by the superconducting ladders in copper oxides 19,20 . However, the question whether the high T c superconductivity appears in the compounds with the three-dimensional lattice or not has never been answered because of the lack of the proper candidate materials. Therefore, the present systems are attractive for systematic studies of the dimensional effects on iron arsenides with FeAs planes; one-dimensional systems such as those in the spin-ladder compound BaFe 2 S 3 18 and its derivatives 28 , two-dimensional systems in the conventional high T c superconductors such as LaFeAsO, and the present three-dimensional systems, Ca n(n+1)/2 (Fe 1−x Pt x ) (2+3n) Pt n(n−1)/2 As (n+1)(n+2)/2 . Although the bulk superconductivity has not been confirmed in the present systems, the presence of the FeAs  layers and the strong Fe-3d characters are common features among iron based superconductors, suggesting the present homologous systems are possible parents for high T c superconductivity with three-dimensional structures.

Methods
Single crystals of the n = 2 and 3 systems were grown by heating a mixture of Ca, FeAs, As, Fe and Pt powders in a composition ratio of Ca/Fe/Pt/As = 6:5:13:12 and 12:11:17:20, respectively. The mixtures were placed in BN crucibles and sealed in an evacuated quartz tube. All manipulation was performed in a glove box filled with nitrogen gas. The ampules were heated at 700 °C for 24 h and then at 1000-1100 °C for 48 h, after which the samples were cooled to room temperature at a rate of 1 K/min. In relation to the structural topology of systems, whisker-shaped single crystals with typical dimensions of 1 × 0.02 × 0.02 mm 3 were successfully obtained, which are clearly different from those in conventional iron-based superconductors with plate-like single crystals. The crystals were characterized by single-crystal X-ray diffraction using the BL02B1 beamline equipped at the SPring-8 synchrotron radiation facility (Japan); the X-ray wavelength was 0.35 Å. The temperature dependence of the crystal structures and the absence of the large amount of the impurity phase in the sample A-D were studied using the BL-8A beamline at the KEK facility (Japan); the X-ray wavelength was 0.69 Å. Powder synchrotron X-ray diffraction experiments were performed using the 11-BM beamline at the Advanced Photon Source facility (U.S.); the X-ray wavelength was 0.4138 Å. The electrical resistivity and magnetization were measured using Quantum Design PPMS and MPMS, respectively, which are equipped at the Institute for Solid State Physics (ISSP), in Japan. Magnetic susceptibility measurement of the n = 3 system under high pressure was performed using a piston-cylinder clamped cell with glycerin as a liquid pressure medium. The applied pressures were determined by the pressure dependence of the superconducting transition temperature of Tin.