Role of valence changes and nanoscale atomic displacements in BiS2-based superconductors

Superconductivity within layered crystal structures has attracted sustained interest among condensed matter community, primarily due to their exotic superconducting properties. EuBiS2F is a newly discovered member in the BiS2-based superconducting family, which shows superconductivity at 0.3 K without extrinsic doping. With 50 at.% Ce substitution for Eu, superconductivity is enhanced with Tc increased up to 2.2 K. However, the mechanisms for the Tc enhancement have not yet been elucidated. In this study, the Ce-doping effect on the self-electron-doped superconductor EuBiS2F was investigated by X-ray absorption spectroscopy (XAS). We have established a relationship between Ce-doping and the Tc enhancement in terms of Eu valence changes and nanoscale atomic displacements. The new finding sheds light on the interplay among superconductivity, charge and local structure in BiS2-based superconductors.

the substantial information of both valence transition and nanoscale atomic displacements, thus XAS has been widely applied in physics and chemistry [19][20][21] . For example, based on the "fingerprint effect", Eu L 3 -edge XANES for EuFe 2 As 2 presents the visually experimental evidence for the pressure-induced valence changes of Eu ions 22 . In addition, Bi L 3 -edge EXAFS were performed to probe the local atomic structure of BiS 2 -based systems 18 . In this contribution, we investigated the local structure of EuBiS 2 F-based system as a function of Ce-doping by XAS, providing the atomic site-selective information of valence changes and nanoscale atomic displacements.

Results
Role of Eu valence changes in the parent and Ce-doped EuBiS 2 F. For the Eu-containing superconductors, detailed investigations of the Eu valence change may provide valuable information on the electronic structure, which is fundamental for a better understanding of their superconductivity 22,23 . Figure 1a shows normalized Eu L 3 -edge XANES data for EuBiS 2 F and Eu 0.5 Ce 0.5 BiS 2 F. The main peak (6975 eV) and the other feature (6983 eV) in the Fig. 1a are associated respectively to Eu 2+ (4f 7 ) and Eu 3+ (4f 6 ) 22 . Now we determine quantitatively the valence of Eu for the parent and Ce-doped EuBiS 2 F by fitting the XANES spectra to an arctangent step function and a Lorentzian peak for each valence state. The mean valence was determined by using a widely used method 24,25 : where I 2+ and I 3+ is integrated intensity of peaks corresponding to Eu 2+ and Eu 3+ on XANES spectrum. Based on the best curve fit in Fig. 1, we estimated the mean valence of Eu ions in EuBiS 2 F is + 2.16(1), instead of + 2, demonstrating the self-electron-doping nature in parent compound without any extrinsic doping. The mean valence of Eu in Ce-doped EuBiS 2 F is + 2.05(1), basically consistent with previous crystallographic and magnetic structure data 15 . Therefore, these data confirm the Eu valence change, suggesting a potential relationship between the Eu valence and superconductivity. In Fig. 2 we focus on the normalized Ce L 3 -edge XANES in Eu 0.5 Ce 0.5 BiS 2 F, in which three main structures A, B and C can be identified. The first peak A around 5728 eV is associated to the transition from the Ce 2p core level to the vacant Ce 5d state mixed with the Ce 4f 1 final state, i.e. Ce 3+ state 26 . On the other hand, the weak feature B around 5745 eV is a characteristic feature of layered rare-earth systems 26 , and its intensity is generally sensitive to the F atom order/disorder in the Eu/CeF layers. The third peak C is the so-called continuum resonance, providing the information on the local lattice structures. It should be noted that the energy difference between the characteristic Ce 3+ (4f 1 ) and Ce 4+ (4f 0 ) absorption peaks is approximately 12 eV, which is independent and is mainly determined by the Ce 2p-4f Coulomb interaction 26 . But in Fig. 2 we found no obvious evidence of Ce 4+ feature around 5740 eV, demonstrating that the Ce valence in the Eu 0.5 Ce 0.5 BiS 2 F sample is essentially trivalent. Considering the valence of Eu, 50 at.% Ce-doping could cause an increment of mean valence for Eu/Ce ions, which increases from + 2.16 of parent EuBiS 2 F to + 2.53 of Ce-doped system. Consequently, additional 17% charges were induced upon Ce-doping in EuBiS 2 F, which is believed to be crucial for the superconductivity enhancement.
Nanoscale atomic displacements in EuBiS 2 F and Eu 0.5 Ce 0.5 BiS 2 F. As is well known, material properties are in a close relationship with its nanoscale atomic structure. Analogous to cuprates and Fe-based superconductors, Ce impurity could alter the local atomic displacements of both blocking layers and BiS 2 superconducting layers. Therefore, to gain an insight into the atomic displacements induced by Ce-doping, we have undertaken detailed structural study by means of Eu and Bi L 3 -edge EXAFS measurements. Figures 3 and 4 display the Fourier transform (FT) magnitudes of the EXAFS oscillations providing real space information at Eu and Bi L 3 -edge, respectively. We have to underline that the positions of the peaks in the FT are shifted a few tenths of Å from the actual interatomic distances because of the EXAFS phase shift 27 . In the BiS 2 layer the in-plane and out-of-plane S atoms are denoted as S1 and S2, respectively. The Eu atom is coordinated with four nearest F atoms at ~2.52 Å and four S2 atoms at ~3.04 Å. Therefore, the broad structure (R = 1.5~3.0 Å) in the FT of Eu L 3 -edge EXAFS corresponds to the contributions of Eu-F and Eu-S2 bonds. On the other hand, the near-neighbor of Bi atoms are one out-of-plane S2 atom at ~2.50 Å and four in-plane S1 atoms at ~2.87 Å. Therefore, the broad structure (R = 1.4~2.6 Å) in Fig. 4 contains information on the Bi-S2 and Bi-S1 bonds. Obviously, large changes in the FTs of both Eu and Bi L 3 -edge can be seen with Ce-doping, indicating the atomic displacements in blocking layers and also in the electronically active BiS 2 layers.
The EXAFS amplitude depends on several factors and is given by the following general equation 28 :   where N j is the number of neighboring atoms at a distance R j , S 0 2 is the passive electron reduction factor, f j (k, R j ) is the backscattering amplitude, λ is the photoelectron mean free path, δ j (k) is the phase shift and σ j 2 is the correlated Debye-Waller factor.
In order to obtain quantitative results, we firstly fit the peaks of EXAFS spectra at Eu L 3 -edge involving contributions of four Eu-F and four Eu-S2 bonds, which were isolated from the FTs with a rectangular window. The range in k space was 3~12 Å −1 and that in R space was 1.5~3.0 Å. Considering the absorption energy at Eu L 3 (6977 eV) and L 2 -edge (7617 eV), the maximum wave-vector k for Eu L 3 -edge EXAFS is up to 12 Å −1 . The spatial resolution ∆ = π R k /2 max 28 is about 0.13 Å with the k max = 12 Å −1 , which is sufficient to distinguish between Eu-F and Eu-S2 bonds. For the least-squares fits, average structure measured by diffraction on EuBiS 2 F system 13 is used as the starting model. The backscattering amplitudes and phase shift were calculated using the FEFF code 29 . Only the radial distances R j and the corresponding σ j 2 were allowed to vary, with coordination numbers N j fixed to the nominal values. The passive electrons reduction factor S 0 2 and photoelectron energy zero E 0 were also fixed after fit trials on different scans. The best values for the S 0 2 were found to be 0.9 and fixed to this value for all the shells. The number of independent parameters which could be determined by EXAFS is limited by the number of the independent data points N ind~( 2Δ kΔ R)/π , where Δ k and Δ R are respectively the ranges of the fit in the k and R space 28 . In our case, N ind is 8 (Δ k = 9 Å −1 , Δ R = 1.5 Å), sufficient to obtain all parameters.
As shown in Table 1, upon Ce-doping the distance of Eu-S2 bond is essentially unchanged within the errors, while the Eu-F distance becomes slightly elongated from 2.51(1) Å to 2.54(1) Å, suggesting a thicker EuF layer induced by Ce-doping. Now we resort to the bond valence sum 30 of Eu (Eu-BVS) using the formula ij 0 , where R 0 is an empirical parameter (2.04 and 2.53 Å for Eu-F and Eu-S bonds 30 , respectively) and  d ij denotes the measured bond distances between Eu and coordinate anions. Here, eight coordinate atoms (four F and four S2 atoms) were considered. Considering the bondlengths achieved from EXAFS fitting, the Eu-BVS value are + 2.14(2) and + 2.07(2) in EuBiS 2 F and Eu 0.5 Ce 0.5 BiS 2 F respectively, essentially in agreement with the valence information retrieved from our XANES data. Meanwhile, Ce-doping also affects the local atomic structure of superconducting BiS 2 layers. In Fig. 4 the broad peaks at Bi L 3 -edge were modelled by two shells, involving contributions of one Bi-S2 and four Bi-S1 bonds, which were isolated from the FTs with a rectangular window. The range in k space was 3~15 Å −1 and that in R space was 1.4~2.6 Å. Spatial resolution ∆ = π R k /2 max is about 0.10 Å, while the number of independent parameters N ind is 9, sufficient to distinguish between Bi-S2 and Bi-S1 bonds and obtain all parameters.
Recently, it was reported that the enhancement of in-plane chemical pressure is responsible for the superconductivity in BiS 2 -based compounds 31 . Upon Ce-doping the sharp contraction of the in-plane Bi-S1 bond (∆ . R 0 11Å, i.e. a higher in-plane chemical pressure) results in an enhancement of the packing density of Bi and S1 ions within the superconducting plane, which would enhance the hybridization of Bi 6p x /6p y -S 3p orbitals and result in an increase of T c . In addition, the fact that in-plane Bi-S1 bondlength decreases with Ce-doping, while the Bi-Bi distance (i.e. a-axis, from 4.0508(1) to 4.0697(1) Å) showing a small increase, indicating the puckering and large in-plane disorder of the Bi-S1 layer. Further information on the atomic disorder can be provided by the correlated Debye-Waller factors (σ 2 ), measuring the mean square relative displacement (MSRD) of the photoabsorber-backscatterer pairs 32 . Data point out that the σ 2 for the in-plane Bi-S1 distance in EuBiS 2 F is anomalously large, demonstrating a large configurational disorder within the Bi-S1 plane. Here, it is worth recalling that the large configurational disorder in BiS 2 plane is quite common in BiS 2 -based superconductors, consistent with the anomalously large diffraction thermal factor of in-plane S1 atom 33 . Upon Ce-doping, the σ 2 for the Bi-S1 bond reduces by 25% with respect to the parent compound, demonstrating that puckering of the Bi-S1 layer seems to be getting reduced; that is to say, a flatter Bi-S1 plane is also responsible for a higher T c . By contrast, the σ 2 for the Bi-S2 bond is quite small and remains unchanged upon Ce-doping, indicating robust Bi 6p z -S 3p hybridizations. All these results suggest that Ce-doping can effectively tune the atomic displacements of BiS 2 superconducting layers.

Discussion
The Ce-doping effect on the valence state and local atomic displacement in the EuBiS 2 F system is investigated by using XAS measurements. First of all, the valence of Eu ions in EuBiS 2 F is estimated to be about + 2.16(1), demonstrating the self-electron-doping nature without any extrinsic doping. Upon 50 at.% Ce-doping, the mean valence of Eu reduces to + 2.05(1) and that of Ce ions are essentially trivalent. The main effect of Ce-doping is to provide additional 17% electrons into the system, beneficial for the superconductivity enhancement. The local atomic displacements can be revealed by Eu and Bi L 3 -edge EXAFS: 1) the in-plane Bi-S1 distance is characterized by a large configurational disorder in EuBiS 2 F-based system, which is quite common in BiS 2 -based superconductors; 2) both the shortening of the in-plane Bi-S1 bond (i.e. a higher in-plane chemical pressure) and the flatter Bi-S1 plane are responsible for an enhancement of superconductivity.
In summary, we established a relationship between Ce-doping and the T c enhancement in EuBiS 2 F-based superconductors, in terms of valence changes and nanoscale atomic displacements. The new findings are promising for providing insights on the interplay of charge, local structure and superconductivity.

Methods
Polycrystalline compounds of EuBiS 2 F and Eu 0.5 Ce 0.5 BiS 2 F were synthesized by solid-state reaction method 13,15 . The samples were well characterized for their phase purity, superconducting and other properties prior to the XAS measurements. The XAS spectra were collected at the BL-14W1 beamline of Shanghai Synchrotron Radiation Facility (SSRF). The storage ring was working at electron energy of 3.5 GeV, and the maximum stored current was about 250 mA. The energy of the incident energy was tuned by scanning a Si (111) double crystal monochromator with energy resolution about 10 −4 . The XAS spectra at Ce L 3 -edge, Eu L 3 -edge, and Bi L 3 -edge were collected with several scans in transmission mode at room temperature. Data reduction was performed using the IFEFFIT program package 34 .