Out-of-Plane Sulfur Distortions in the Bi4O4S3 Superconductor

The local atomic structure of the non-magnetic layered superconductor Bi4O4S3 was investigated using neutron diffraction and pair density function (PDF) analysis. Although on average, the crystal structure is well ordered, evidence for local, out–of–plane sulfur distortions is provided, which may act as a conduit for charge transfer from the SO4 blocks into the superconducting BiS2 planes. In contrast with LaO1−xFxBiS2, no sulfur distortions were detected in the planes, which indicates that charge density wave fluctuations are not supported in Bi4O4S3.


Introduction
Superconductors with competing ground states have been extensively studied ever since the discovery of the cuprates [1]. Most of the recent interest has been in materials whose parent ground state is magnetic. The bismuth sulfide class of superconductors [2][3][4][5][6][7][8], although not magnetic, is a test bed for investigating the effects of charge density wave (CDW) instabilities [9,10], lattice modes leading to phonon softening [9], and spin-orbit (SO) interactions [11,12] on the superconducting mechanism. The BiS 2 superconductors exhibit strong electronic correlations [11]. Density functional theory calculations suggested that spin polarization is present even though the crystal lattice is centrosymmetric [10,11]. Given its quasi-two-dimensional nature, BiS 2 may exhibit SO coupling without breaking crystal inversion symmetry, but instead driven by atomic site asymmetry [11].
Two kinds of superconductors were discovered in the earlier stage, Bi 6 O 4 S 4 (SO 4 ) 1−x [2] and LnO 1−x F x BiS 2 with Ln = Pr, Ce, La, and Yb [3,13]. The former consists of a sulfate layer where vacancies and crystal defects are common. The structure is analogous to that of LaOFeAs, an Fe-based superconductor [14]. Superconductivity occurs in the BiS 2 layer that has vacancies, while in the latter, crystal defects induced under pressure have been linked to a higher T c . The LnO 1−x F x BiS 2 system exhibits a peculiar relationship between its structural and superconducting properties where doping with F brings significant disorder to the crystal structure, as well as inducing superconductivity.
In the BiS 2 system, the dominant carriers arise from the Bi 6p orbitals that strongly hybridize with the S 3p orbitals near the Fermi surface. A CDW instability has been proposed in LnO 1−x F x BiS 2 that arises from a (π, π, 0) mode, which corresponds to in-plane displacements of S atoms around the M point [10]. This was verified experimentally in our previous work in [15] on LaO 1−x F x BiS 2 . The xy-mode of S displacements breaks the long-range symmetry, indicating a long-range CDW state. Whether or not these kinds of distortions exist in the Bi 6 O 4 S 4 (SO 4 ) 1−x class of materials has not been investigated. The (SO 4 )-deficient compound Bi 4 O 4 S 3 corresponding to x = 0.5 is superconducting with T c = 4.5 K [2,16]. Using neutron scattering and pair density function (PDF) analysis, we verified the absence of in-plane S displacements in the BiS 2 superconducting plane of Bi 4 O 4 S 3 . This finding points to the absence of the CDW instability, as proposed in LaO 1−x F x BiS 2 . Instead, an out-of-plane S displacement along the c-axis (0.29 Å in magnitude) is observed, which may lead to a possible charge transfer mechanism from the charge reservoir layers to the superconducting Bi planes. This motion is reminiscent of what was proposed in the cuprate-based superconductor, YBa 2 Cu 3 O 7−δ , in which oxygen motion in the chains above the superconducting CuO 2 layer was attributed to charge transfer [17][18][19]. The role of out-of-plane S displacement in the charge transfer mechanism for self-doping of the active BiS 2 -layer has been reported in other BiS 2 -based superconductors as well [20,21].

Results and Discussion
Bi 4 O 4 S 3 has a tetragonal crystal structure with the I4/mmm space group and lattice parameters a = b = 3.981 Å and c = 41.466 Å. The refinement results with the neutron powder diffraction data at 2 K fit well using the tetragonal structure. The results are shown in Figure 1a, with a goodness of fit parameter of R w = 0.05. The powder sample contained additional phases of Bi 2 S 3 and unreacted bismuth. Shown in Figure 1b is the unit cell of Bi 4 O 4 S 3 with the BiS 2 planes. The three S atom positions along the c axis are labeled S1, S2, and S3, as shown in the diagram for the unit cell. The S2 atoms in the BiS 2 layers lie on the same plane as the Bi atoms, whereas the S1 atom is above the BiS 2 layer, at the apical site. The S3 atoms are part of the SO 4 layer at z = 0.5, which is sandwiched by the Bi 2 O 2 layers. Defects of SO 4 Figure 2a,b is the temperature dependence of the a and c lattice constants, respectively, obtained from the average structure refinement. Both the a and c lattice constants increase with temperature due to thermal expansion. Figure 2c shows the position z along the c axis within the unit cell for the S1 atom as a function of temperature. The z coordinate is plotted as obtained from both the average and local structure refinement results. The local structure was determined from the PDF by Fourier transforming the powder diffraction spectrum (Bragg peaks + diffuse scattering) into the real space (see the Methods Section). It can be seen that the z coordinate obtained from the local structure refinement is consistently higher than the one obtained from the average crystal structure refinement, which will be explored further. However, the larger uncertainty in z from PDF refinement suggests that we cannot make inferences on the temperature dependence of the S1 atom displacements from the PDF analysis.

Shown in
Shown in Figure 2d is the magnetization (M) as a function of temperature in the presence of an applied magnetic field of 10 Oe below 6 K. A large increase in the diamagnetic response of the sample is seen below ∼4.5 K in the zero-field-cooled (ZFC) magnetization, indicating the onset of superconductivity, in agreement with previous reports [2].  Figure 3 shows the results of the PDF analysis, which provides information on the local arrangement of atoms in the real space and is very sensitive to short-range distortions [22,23]. Shown in Figure 3a is a comparison of the reduced pair distribution function G(r) obtained from the experimental data (for Bi 4 O 4 S 3 at 2 K) to G(r) calculated from the "average" model based on the structural parameters obtained from Rietveld refinement. The splitting of the peak at ∼3 Å, which corresponds to S atom correlations with other atoms, cannot be reproduced using this average model. Figure 3c shows the same experimental data as in Figure 3a, but comparing to a "local" model of G(r) where the S1 and S2 atoms are displaced along the c axis by 0.29 Å and 0.05 Å, respectively. (The calculated peaks below r = 2 Å arising from the atom correlations within the sulfate layer are comparable to the noise level of the experimental data.) Figure 3b shows the difference between the average and local models, with arrows marking the displacements of the apical sulfur atom towards the BiS 2 layers in the local model relative to the average model. There is good agreement between the data and the local model. In particular, the splitting of the second peak was reproduced after the apical S atom was displaced from the average-model position. In the local model, the Bi-S bond becomes shorter and the S1 atom moves further from the Bi 2 O 2 layer towards the superconducting BiS 2 planes as compared to the average model. This suggests the presence of a charge transfer mechanism, which is reminiscent of what is observed in other layered superconducting systems such as YBa 2 Cu 3 O 7−δ (YBCO), where the oxygen atom movement towards the CuO 2 planes has been explored [17]. Charge fluctuations are known to exist in materials belonging to the family of BiS 2 superconductors. LaO 1−x F x BiS 2 , for instance, shows in-plane short-range distortions of sulfur atoms [15,24]. In Bi 4 O 4 S 3 , however, the BiS 2 layer is robust, and no evidence for in-plane distortions or charge fluctuations were found in contrast to other BiS 2 -based superconductors. The effects of the lattice vibrations on the PDF peak widths were modeled using the correlated Debye model [25,26] (see the Methods Section), and the Debye temperature for Bi 4 O 4 S 3 was estimated by studying the mean-squared relative displacements of atomic pair motion as a function of temperature. The PDF peak width FWHM (σ) values from the experimental data were extracted by fitting Gaussian functions to the Bi-O atom pair nearest neighbor correlation peak. Shown in Figure 4 is the temperature dependence of σ 2 fit using the correlated Debye model. The Debye temperature, θ D , from the model was determined to be 368 K.

Materials and Methods
Polycrystalline samples of Bi 4 O 4 S 3 were prepared by the solid state reaction method using Bi, S, and Bi 2 O 3 . The details of the sample preparation were reported in [2]. The temperature dependence of the magnetic susceptibility from 2 K to 6 K was measured in the zero-field-cooled (ZFC) and field-cooled (FC) modes using a superconducting quantum interference device (SQUID) magnetometer with a 10 Oe applied magnetic field.
The time-of-flight (TOF) neutron diffraction experiment was carried out at the Nanoscale Ordered Materials Diffractometer (NOMAD) at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (ORNL). The data were analyzed using Rietveld refinement to find parameters characterizing the crystal structure [27], resulting in what we label the "average model". The PDF analysis [28,29], which provides information on the local arrangement of atoms in the real space without the assumption of periodicity, was performed on the same neutron diffraction data used for the Rietveld refinement. NOMAD is a diffractometer with a large bandwidth of momentum transfer Q, and it provides the total structure function S(Q). S(Q) was Fourier transformed into the real space, as shown in Equation (1), to obtain G(r) [30,31].
The instrument background and empty sample can were subtracted from S(Q), and the data were normalized by vanadium. A maximum Q of 40 Å −1 was used. G(r) corresponds to the probability of finding a particular pair of atoms with an inter-atomic distance r [32].
The crystal structure models were generated using the VESTA software [33]. The correlated Debye model [25,26,34] was used to find the Debye temperature, θ D , from the temperature dependence of PDF peak widths. Using Equation (2), the full-width at half-maximum (FWHM), defined as σ ij , was extracted from the PDF peak corresponding to the Bi-O nearest neighbor correlations. Here, the Debye wavevector is given by k D = (6π 2 N/V) 1/3 , where N/V is the number density of the crystal; the Debye cutoff fre-

Conclusions
The crystal structure and local atomic distortions in the layered superconductor Bi 4 O 4 S 3 were investigated as a function of temperature. The lattice undergoes a thermal expansion in the temperature range from 2 K to 300 K in both the in-plane and out-of-plane directions. While the average crystal structure is consistent with the I4/mmm space group symmetry across the temperature range, the local structure analysis revealed that the apical S1 atoms move up by 0.29 Å toward the superconducting BiS 2 planes, suggesting a charge transfer mechanism.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.