New insight on the properties of the superconducting iron spin ladder BaFe₂S₃

Abstract

{\mathrm{B}\mathrm{a}\mathrm{F}\mathrm{e}}_2{\mathrm{S}}_3 and {\mathrm{B}\mathrm{a}\mathrm{F}\mathrm{e}}_2{\mathrm{S}\mathrm{e}}_3 are the only two quasi-one-dimensional iron-based compounds that become superconductors under pressure. Interestingly, these two compounds exhibit different symmetries and properties. While more detailed and recent studies on {\mathrm{B}\mathrm{a}\mathrm{F}\mathrm{e}}_2{\mathrm{S}\mathrm{e}}_3 using single crystals have advanced the field towards a more universal description of this family, such a study is still lacking for the compound {\mathrm{B}\mathrm{a}\mathrm{F}\mathrm{e}}_2{\mathrm{S}}_3. Here, we present a detailed study of the crystalline and magnetic structures performed on single crystals using X-ray and neutron diffraction. We demonstrate a polar structure at room temperature within the Cm2m space group, followed by a structural transition at T_S = 130 K to the polar Pb{2}_{1}m space group. This space group remains unchanged across the magnetic transition at T_N = 95 K, revealing multiferroic characteristics with a weak magnetoelastic coupling. The determined magnetic structure is monoclinic (P_{a}m), with non-collinear Fe magnetic moments, tilted from the rung axis. This reexamination of the temperature-dependent properties of {\mathrm{B}\mathrm{a}\mathrm{F}\mathrm{e}}_2{\mathrm{S}}_3 provides new insights into the physics of this system from multiple key perspectives.

Graphical abstract

Keywords

multiferroicity / phase transition / strong correlation

1 Introduction

Unconventional superconductivity has been captivating physicists since its discovery in cuprates in 1986. From the copper age, we transitioned into the iron age during the 2000s with the discovery of a large number of families of iron based pnictides [1]. A common feature of all these systems is their two-dimensional nature. More recently, it has been found that the dimensionality of these iron-based compounds can be further reduced to yield quasi-one-dimensional bands, forming ladder structures, and achieving superconductivity under pressure [2-4]. These compounds constitute a distinct family of iron chalcogenides with the general formula BaFe₂X₃ (where X is S or Se). In these systems, theoretical descriptions can be strongly facilitated by the low dimensional character of the electronic structure. The ultimate goal is to evidence a possible universal character in the series to elucidate the mechanism underlying high Tc superconductivity. This requires revealing the relevant parameters that describe these compounds, namely the active degrees of freedom and the couplings that cannot be neglected. In this family of materials, these relevant parameters are naturally the exact crystal structure, which determines the symmetries of the Hamiltonian, and the accurate magnetic order, whose fluctuations can be involved in the the superconducting mechanism, and which can couple to the structure via magneto-elastic or magneto-electric effects.

Previous powder X-ray experiments [2, 5] have shown that BaFe₂S₃ crystallizes in the Cmcm space group (unit cell parameters a=8.787(1) Å, b=11.225(1) Å, and c=5.288(1) Å at 300 K) with two Fe ladders of edge-sharing FeS₄ tetrahedra along the c axis, composing the unit cell. The two ladders are equivalent by translation, unlike the Se parent compound, which crystallizes in the non-standard Pbnm space group (using the same unit cell setting) [6, 7]. BaFe₂S₃ is a Mott semiconductor with a small band gap of around 40−60 meV. Below T_N, a magnetic transition is observed in neutron diffraction experiments [2, 8]. In contrast to BaFe₂Se₃, which stabilizes an original block-like antiferromagnetic (AFM) order at ambient pressure [9], the magnetic order of BaFe₂S₃ is stripe-like, with a propagation wave vector \mathit{k}=(\frac{1}{2},\frac{1}{2},0), similar to that observed for KFe₂S₃ [10] and CsFe₂S₃ [8]. The ordered moments align along the a-axis and reach 1.1 \pm 0.1 {\mu }_B per Fe atom at low temperature. This moment is significantly below the expected one for a high-spin Fe(II) atom (S=2) of 4 {\mu }_B. This reduction in moment could be attributed to a disordered spin contribution (spin glass part), an Orbital-Selective-Mott-Phase [11] or possible stoichiometry issue. In fact the Fe deficiency BaFe{}_{2-\delta }{S}_3, is shown to influence the magnetic properties, inducing a non-monotonous variation of T_N from 80 K (\delta = −0.1) to 122 K (\delta = 0.1) and a possible modification of the amplitude of the moment [2, 12]. A comprehensive structural and magnetic investigation based on well characterized high-quality single-crystals is essential to provide an exact description of BaFe₂S₃ as performed recently for BaFe₂Se₃.

Indeed, inspired by a theoretical work [13], recent comprehensive studies of the properties of BaFe₂Se₃, made possible by measurements on single crystal that avoid missing fine effects, enabled the detailed knowledge of the structural [14, 15], dielectric [16], and magnetic [17-19] properties, as well as their couplings. It evidenced a multiferroic character close to room temperature and identified a stripe-like magnetic phase similar to the one of BaFe₂S₃ near the superconducting dome under pressure. This is the fingerprint of a remarkable universal character within the family [20]. To further understand these compounds in a unified formalism, a similar investigation for BaFe₂S₃ is necessary.

In this paper, we thus present a comprehensive study of the BaFe₂S₃ crystalline and magnetic structures as a function of temperature, combining X-ray and neutron diffraction on high-quality single crystals. Our results provide a wealth of new and crucial information on this compound with unprecedented details. We show that BaFe₂S₃ is in fact non-centrosymmetric at room temperature, and its symmetry is further reduced below a new transition at T_S=130 K, which results in a primitive unit cell comprising two inequivalent ladders. This new unit cell is preserved down to 17 K, showing only a weak coupling with the magnetic order below T_N. Nevertheless, this confirms its multiferroic character. The magnetic structure obtained is monoclinic and slightly deviates from the antiferromagnetic structure reported in the literature [2], with non-collinear magnetic moments, tilted from the rung direction. The succession of structural and magnetic phase transitions, is the indication of structural instabilities which could be associated to the low dimensionality of the system. This brings new insight in the understanding of the state precursor of the superconducting phase.

2 Samples and experimental methods

2.1 Synthesis and characterization

BaFe₂S₃ crystals were grown from the melt using the self-flux method [21], starting from a mixture of BaS:Fe:S (99.9%), Fe (99.9%), and S (99.999%) powders with a BaS:Fe ratio of 1:2.05:3. Two grams of the reagents were pelletized, placed in a carbon crucible, and then sealed in an evacuated quartz tube with a partial pressure of 300 mbar of Ar gas. The quartz tube was placed in a vertical tubular furnace, annealed at 1100 °C for 24 hours, and then cooled down to 750 °C at a rate of 6 °C/h before finally cooling to room temperature. This process resulted in a centimeter-sized pellet consisting of intimately co-aligned millimeter-sized rod-shaped crystals along the c direction. The powder X-ray analysis of the ground rod-shaped crystals show that the sample corresponds to the BaFe₂S₃ phase with absence of impurities.

The chemical composition of the products was analyzed by energy dispersive X-ray spectrometer equipped with a scanning electron microscopy (SEM/EDX). We took an average of chemical compositions of 15 points for two single crystals and obtained a Fe stoichiometry of 2.10\pm 0.05.

The atomic structure of the BaFe₂S₃ single crystals was further investigated down to the atomic scale by Scanning Transmission Electron Microscopy (STEM). High-angle annular dark-field (HAADF) images were acquired at room temperature using a C3/C5-corrected Nion UltraSTEM 200 operating at 100 kV with a 30 mrad convergence angle and a probe current of about 50 pA. Cross-sectional electron-transparent samples were prepared for STEM studies by focused ion beam on a SCIOS dual beam platform (FEI-Thermofischer) according to the standard procedure.

Both the (a,c) and tilted (a,c) planes of a BaFe₂S₃ single crystal were investigated using HAADF-STEM images acquired at different magnifications: see Fig. 1. The (a), (b) and (c) parts of Fig. 1 present the BaFe₂S₃ lattice along the (a, c) plane where the bright HAADF contrast correspond to the Ba/S atomic columns while the intermediate Fe/S atoms chains could not be imaged in that orientation. In (f), the atomically-resolved HAADF-STEM image of the BaFe₂S₃ lattice confirms the expected atomic structure [see inset Fig. 1(f)] between the brighter contrast belonging to the Ba/S atomic columns and the darkers ones assigned to the single Fe columns. At lower magnification in Figs. 1(d) and (e), the quality of the atomic arrangement can be appreciated on a larger scale. A few large stained contrasts can be observed in Figs. 1(d) and (e), corresponding to some FIB redeposition on the surface during lamella preparation. In comparison with the parent compound, i.e., BaFe₂Se₃, previously studied down to the atomic scale as well [22], the BaFe₂S₃ system here does not evidence any structural issue and planar faults as confirmed by both planes’ observations.

2.2 Experimental methods

We conducted single-crystal and powder X-ray diffraction experiments at the SOLEIL synchrotron on the CRISTAL beamline. For single-crystal measurements, we used a Newport four-circle diffractometer equipped with a Rigaku Oxford Diffraction Atlas CCD detector at a wavelength around 0.6706 Å issued from a Si(111)-Double Crystal Monochromator. Selected single crystals, typically tens of microns in size, were measured at a wavelength of \lambda = 0.6706 Å at 300 K and 144 K using a nitrogen blower and at 95 K and 17 K using an helium blower. About 15,000 reflections were measured for each temperature. For the experiment on powder, we used a wavelength of 0.5818 Å and a two circle-diffractometer equipped with a closed-cycle cryostat as well as a 20 crystals analyser. Refinement of the crystallographic structure was performed using the Jana software [23]. The introduction of twins did not improved the refinement and led to a twin ratio of 50%, so we worked only with one crystallographic domain.

Neutron diffraction experiments were performed at 2 K on a millimeter-sized single crystal using the D9 hot neutron four-circle diffractometer at the Institut Laue-Langevin (ILL), Grenoble, France, with \lambda =0.836 Å using the (220) plane of a Cu crystal monochromator; \lambda /2 contamination was avoided by including an Er absorption filter in the transmission geometry. The nuclear and magnetic reflections were collected at 2 K. Integrated intensities of Bragg reflections were collected with standard \omega scans for low q reflections and \omega−2\theta scans for medium and high q reflections. Powder neutron experiments as a function of temperature were performed on the D1B spectrometer at ILL with an incident wavelength \lambda =2.52 Å. Refinement of the magnetic structure was performed using the Fullprof program [24].

3 Results

3.1 Structural properties

To accurately investigate the ambient temperature structure, we measured the 300 K X-ray pattern of BaFe₂S₃. We observed that it exhibits intensity at (h0l) positions with l=2n+1, typically three orders of magnitude smaller than other Bragg reflections, forbidden by the glide mirror c perpendicular to b as seen in Fig. 2(a). This cannot be attributed to multiple scattering since the extinctions associated with C centering [(hkl) with h+k=2n] remain intact. Similar observations were made at 140 K. Consequently, we conclude that the Cmcm space group represents only an average structure. Among the three orthorhombic subgroups, only Cm2m (Amm2 in the standard setting) is compatible with the extinction rules observed in the measurements. Notably, breaking the c glide mirror allows the two Fe-Fe bonds along the ladder to differ. The results of our refinement, presented in the supplemental information [25], show that this difference is insignificant within the uncertainties at 300 K (2.635(10) and 2.638(10) Å) but a bit larger at 140 K (2.617(10) and 2.643(10) Å).

At 95 K and 17 K, we observe a significant intensity, about 10% of typical Bragg reflections, at positions forbidden by C centering, specifically for h+k=2n+1, as visible in Fig. 2(b). However, systematic extinctions remain observed at (0kl) and (0k0) positions for odd k, corresponding to the presence of a b glide mirror perpendicular to a and a 2_1 helical axis along b. The observation of additional structural effects in the X-ray pattern is the fingerprint of a structural transition. Interestingly, this transition is not preceded by quasi-1D pretransitional fluctuations such as expected for Spin−Peierls transitions. Assuming this is a second-order structural transition, as we will demonstrate later, only Pb{2}_{1}m (Pmc{2}_1 in the standard setting) is compatible with these symmetry elements among the four subgroups of Cm2m. The refined atomic positions in this space group for all temperatures are provided in the Electronic Supplementary Materials [26]. The data collected and used, as well as the results of the refinements selected for the correct space groups, are summarized in Table 1. The comparison of the low temperature structures with the 140 K one shows that the two ladders of the unit cell rotate along their long axis but in opposite ways. This leads to the loss of the C centering as for BaFe₂Se₃. The Fe displacements of about 0.02 Å along the b direction are accompanied by Ba movements of 0.04 Å mainly along a. As for the Fe−Fe distances along the ladder, below T_S, they are identical within the error bars.

3.2 Results from neutron scattering

The parent compound BaFe₂Se₃ exhibits strong magneto-elastic coupling [14, 15], which can be an important parameter to understand the properties of these family of superconductors. We have thus examined the case of BaFe₂S₃ and in particular the effect of the magnetic transition on the structural properties using neutron diffraction. To this end, using single crystal neutron diffraction, we measured the evolution of a magnetic Bragg peak (\frac{1}{2}\overline{\frac{1}{2}}1) and two nuclear Bragg reflections breaking the C-centering, (1\overline{8}0) and (410). As shown in Fig. 3(a), the temperature dependence of these peaks, proportional to the square of the magnetic and structural order parameters (ordered moment and atomic displacement respectively), indicates a second-order transition. The obtained critical temperature and critical exponent values are T_N = 95 \pm 3 K and \beta = 0.16 \pm 0.1 for the magnetic transition, and T_S = 130 \pm 5 K and \beta = 0.35 \pm 0.1 for the structural transition. It is noteworthy that a weak magnetic intensity persists above T_N, likely due to pretransitional fluctuations expected in a low-dimensional system. Furthermore, no visible anomaly at T_N was observed in the evolution of the nuclear peak within the error bars, suggesting weak magneto-elastic coupling in this compound. This finding is corroborated by our temperature-dependent powder neutron diffraction measurements showing no anomalies in lattice parameters across the magnetic transition. Surprisingly, the lattice parameters also show no significant changes at the structural transition.

To obtain a better resolution of the thermal evolution of the lattice parameters through both the structural and magnetic transitions, we performed powder diffraction experiments using X-rays. We report the evolution of the lattice parameters as a function of temperature, derived from the measurement of the position of the (200), (060) and (002) Bragg peaks, in Figs. 3(b)−(d). With this improved precision, we observe a change in slope around the structural transition temperature T_S = 130 K, and an anomaly near the magnetic transition temperature T_N = 95 K mainly visible along the ladder c direction. This indicates a weak but non-zero magneto-elastic coupling.

We then extended our study of BaFe₂S₃ by collecting 139 magnetic reflections from a single crystal to resolve the magnetic structure at 2 K. We performed a refinement using the room temperature space group Cm2m to reduce the number of parameters and constrain the fit. This approach is justified by the fact that the distortions between the Cm2m and Pb{2}_{1}m structures are sufficiently small not to affect the magnetic order. A symmetry analysis starting from the Cm2m group with a propagation vector (\frac{1}{2},\frac{1}{2},0) proposes two irreducible representations, both one-dimensional. In both cases, the Fe site from the parent space group splits into two distinct orbits, indicating that the magnetic moments at each site are no longer constrained by symmetry. However, because of the similar environments and oxidation states of the Fe ions, their spins should be identical and will be forced to be identical in the following. Based on representational analysis, these two irreducible representations correspond to the magnetic space groups P_{a}m and P_{c}c (BNS notation). The model described in the P_{a}m magnetic space group provides the best fit to the experimental data (R_B = 16.3% for P_{a}m and R_B = 315% for P_{a}c) and is the only one corresponding to a stripe-like magnetic structure with antiferromagnetic order along the ladder. It presents a non-colinear character with spins in the ladder plane but tilted by \pm {20}^{\circ } from the a axis. This is slightly different from the structures proposed in the literature in which the spins are perfectly aligned on the rung of the ladders [2].

To verify the magnetic model, a simulated annealing (SA) procedure was performed using a triclinic model with four Fe spins. The results quickly indicated two distinct Fe spin groups, which led us to constrain certain angles between these moments. Several angle constraints yielding similar fits are represented in Fig. 4. Magnetic space groups were determined using ISOCIF, capable of detecting the highest symmetry taking into account the experimental error bar. Among the tested models, b) provides the best fit and a symmetry in agreement with the previous symmetry analysis. It also closely matches our previously proposed tilted spin structures thus confirming the final magnetic model. The results for this particular case are detailed in Table 2.

Similar to previous publications [2, 8], the magnetic structure obtained corresponds to a stripe-like magnetic order but with a tilt of the Fe moments of 20° from the rung direction. This tilt recalls the one observed in the parent Se compound [27, 28] which was attributed to a significant role of the local crystallographic anisotropy [28]. However, in BaFe₂S₃, the spin orientation within the (a,c) plane does not appear to be associated with any relevant crystallographic direction. Regarding the inter-ladder arrangement, we observe that the ladders are antiferromagnetically aligned along the a+b diagonal and ferromagnetically aligned along the a-b diagonal (see Fig. 4), highlighting the monoclinic nature of this structure.

4 Discussion

The temperature-dependent properties of BaFe₂S₃ have been thoroughly revisited, putting the physics of this system into perspective on several key aspects. Firstly, we discovered a structural transition at T_S = 130 K separated from the magnetic ordering T_N. The absence of significant Fe bonds dimerization as well as the stabilization of a magnetic transition at low temperature exclude a Spin-Peierls origin. This result suggests a reconsideration of the anomaly in dielectric and transport properties at this temperature, which had previously been attributed to a unique magnetic transition [3, 29]. Secondly, the discovery of a polar Cm2m space group at room temperature that persists below the structural transition temperature T_S and within the magnetic phase below T_N = 95 K. This endows the compound with multiferroic characteristics. With its relatively small band gap [3], the electric polarization of BaFe₂S₃ expected from its non-centrosymmetric space group is difficult to measure, likely screened by conduction electrons [29]. The nature of its multiferroicity, therefore, lies at the interface between classical magnetoelectric insulating compounds [30] and metallic multiferroic materials with novel fundamental physics and unusual properties for practical applications [31]. Thirdly, the low temperature magnetic structure we determined not only does differ from the block-like magnetic order of BaFe₂Se₃ but also slightly differs from the previously published antiferromagnetic structure [2, 8]. Specifically, the Fe moments present a tilt of 20° from the rung of the ladder which is above the error bars. It is now interesting to compare the two Fe ladders compounds. A weaker magnetic frustration is present in the S compound primarily evidenced by its stripe-like magnetic structure compared to the block-like order of BaFe₂Se₃ composed of the emblematic up-up-down-down spin arrangement along the legs of the ladder. In the Se system, the frustration is attributed to a strong next-nearest-neighbor AFM coupling [18] and leads to a magneto-structural coupling through both an exchange-striction mechanism and the inverse Dzyaloshinskii–Moriya interaction due to the chiral order. These effects are much weaker in BaFe₂S₃ which explains the weak magneto-elastic coupling reported here. Our results shed new light on the properties of BaFe₂S₃ at ambient pressure. The observed succession of structural and magnetic transitions constitutes a very different phase diagram to that previously proposed. Identifying these phases in competition with superconductivity under pressure is essential. Our work presents an intensive study of these new phases and shows that they correspond neither to a Spin−Peierls transition, nor to a standard stripe-like phase. We are currently investigating the role of orbital order in this phase diagram.

5 Conclusion

These results provide a new foundation for studying this compound and its parent Se compound. Notably, investigating the lattice dynamics of this compound could provide insights not accessible via diffraction, similar to what has been done in BaFe₂Se₃ [15]. It also calls for a reexamination of the actual structure under pressure, particularly regarding the persistence of the non-centrosymmetric character into the superconducting phase, potentially paving the way for a one-dimensional non-centrosymmetric superconductor.

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