The discovery of iron-based superconductors promotes the development of studies on iron-based materials.^[1–6] In the past decade, different kinds of iron-based compounds are reported and they can be classified according to the dimensionality of structural unit formed by the FeX₄ (X = pnictogens and chalcogens) tetrahedra. Most of iron-based superconductors, such as LaOFeAs, BaFe₂As₂, FeSe, (Li_1−xFe_x)OHFeSe, and Li_x(NH₃)_yFe₂Se₂,^[1,2,6–9] share common two-dimensional (2D) FeX layers built up with edge-sharing FeX₄ tetrahedra.^[10] When FeX₄ tetrahedra connect each other along one crystallographic axis via edge sharing, they can form quasi-one-dimensional (quasi-1D) compounds such as KFeS₂ with single 1D FeS₄ chain along the c axis,^[11] BaFe₂S₃ and BaFe₂Se₃ with double 1D FeS₄ or FeSe₄ chains (spin-ladder structure) along the b axis.^[12–14] The latter compounds exhibit Mott insulating behaviors with antiferromagnetic (AFM) orders at ambient pressure.^[12–14] Interestingly, both of BaFe₂S₃ and BaFe₂Se₃ show superconductivity under pressure.^[15–17] Moreover, the connected edge-sharing FeX₄ tetrahedra can also form three-dimensional (3D) compounds like CaFe₄As₃.^[18] It displays non-Fermi-liquid behavior at zero field with enhanced electron–electron correlations.^[18] Thus, exploration of iron-based compounds with various dimensionality of FeX₄ units would provide a comprehensive understanding of the relation between electronic correlation and dimensionality in the iron-based materials.

When compared to the extensively studied ternary compounds, the studies on quaternary iron-based compounds are still rare so far. Recently, the quaternary compounds Ba₂PnFeCh₅ (Pn = Sb, Bi, and Ch = S, Se) containing isolated (zero-dimensional, 0D) FeCh₄ tetrahedra are reported.^[19–21] Previous studies indicate that they exhibit AFM order at low temperature in general.^[19–21] In this work, we have grown the single crystal of Ba₂BiFeS₅ and carried out a detailed study on physical properties. It shows a long-range AFM order with Neel temperature T_N∼30 K, and there may be an AFM fluctuation before the formation of longe-range antiferromagnetism.

Single crystals of Ba₂BiFeS₅ were grown by solid state reaction method. Ba pieces (99.9%), Bi shots (99.99%), Fe lumps (99.98%), and S granules (99.999%) were mixed with a stoichiometric molar ratio Ba:Bi:Fe:S = 2:1:1:5. The mixture was loaded in an alumina crucible which was put into a quartz tube. These operations were handled in the glovebox with the O₂ and H₂O contents under 0.1 ppm. Then the quartz tube was sealed with Ar gas under the pressure of 0.2 atmospheres. The sealed tube was heated up to 1273 K for 24 h and kept at 1273 K for 48 h. Then it was cooled down to 673 K with 3 K/h before finally switching off the furnace. The crystals can be extracted from the matrix mechanically. X-ray diffraction (XRD) patterns were collected using a Bruker D8 X-ray Diffractometer with Cu radiation (λ = 1.5418 Å) at room temperature. The lattice parameters were obtained by fitting the powder XRD pattern using the TOPAS4 software.^[22] The elemental analysis was performed using an energy-dispersive x-ray spectroscopy (EDX) in a JEOL JSM-6500 scanning electron microscope. Magnetization measurements were performed in a Quantum Design Magnetic Property Measurement System (MPMS3). Heat capacity measurements were performed in Quantum Design PPMS-14.

Figure 1(a) shows the structure of Ba₂BiFeS₅. The structure is formed by alternatively stacking Fe–Bi–S layers and Ba²⁺ cations along the a axis. The main building blocks of a Fe–Bi–S layer in the bc plane are FeS₄ tetrahedra and BiS₅ quadrangular pyramids. As shown in Fig. 1(b), the 1D connected chain of BiS₅ along the b axis consists of edge-sharing BiS₅ quadrangular pyramids. Via edge sharing, FeS₄ tetrahedra connect on both sides of this chain along the c axis alternatively with the atomic distance . On the other hand, the shortest atomic distance between two Fe ions in the neighboring Fe–Bi–S chains is very large (∼5.8 Å), comparable with the interchain distance of Fe ions in BaFe₂S₃ (∼5.86 Å).^[12] Thus, FeS₄ tetrahedron in Ba₂BiFeS₅ can be viewed as a 0D unit. Figure 1(c) shows the powder x-ray diffraction pattern of the ground crystals and it is found that this pattern can be well fitted by the Rietveld method using the reported structure of Ba₂BiFeS₅ (space group Pnma) with minor second phase BaBi₂S₄ (∼6.9(1) wt%). It is hard to eliminate the minority phase of BaBi₂S₄ because it is very stable and its formation temperature overlaps with Ba₂BiFeS₅.^[23] The refined lattice parameters are a = 12.1378(7) Å, b = 8.9419(4) Å, and c = 8.8294(5) Å. These values are close to previous results^[19] but slightly smaller than those in Ba₂BiFeSe₅,^[20,21] which can be ascribed to the smaller ionic size of S than Se. The analysis of EDX result shown in Fig. 1(d) confirms the existence of Ba, Bi, Fe, and S. The obtained ratio of Ba:Bi:Fe:S is 2.17(3):0.99(6):1:5.34(3) when setting the content of Fe as 1, consistent with the chemical formula of Ba₂BiFeS₅. The inset of Fig. 1(d) displays the photograph of typical crystals of Ba₂BiFeS₅. They have a sub-millimeter size with black color. The subquadrate shape is in agreement with the crystallographic symmetry of Ba₂BiFeS₅.

Fig. 1.

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Fig. 1. (a) Crystal structure of Ba2BiFeS5. The white, orange, dark green, and yellow balls represent Ba, Fe, Bi, and S atoms, respectively. (b) Structural unit of an infinite chain arranged in the bc plane. The shortest atomic distances of intrachain Fe–Bi and interchain Fe–Fe are marked. (c) Powder XRD pattern of crushed Ba2BiFeS5 single crystals. The black and red line represents the observed and calculated pattern, respectively, and the green line shows the difference between them. The black and blue bars represent the peak portions of Ba2BiFeS5 and the minor second phase BaBi2S4, respectively. (d) The EDX spectrum of Ba2BiFeS5 single crystal. Inset: photo of obtained Ba2BiFeS5 single crystals. The length of one grid in the photo is 1 mm.

Temperature dependence of magnetization M(T) for several pieces of Ba₂BiFeS₅ crystals at T is shown in Fig. 2(a). It can be seen that the M(T) increases as the temperature decreases from 300 K to 35 K. There is a sudden drop when lowering temperature further, suggesting that there is an AFM transition in Ba₂BiFeS₅. The determined AFM transition temperature T_N from the peak of curve with zero-field cooling mode is 30.1 K (the inset of Fig. 2(a)),^[24] which is consistent with the pervious report.^[19] When , there is a similar drop in the field-cooling (FC) M(T) curve, implying the absence of magnetic glassy state. When , there are upturns appearing in both ZFC and FC M(T) curves, possibly due to the contribution of minor impurities in the sample. For , the inverse of magnetic susceptibility exhibits the nearly linear behavior up to 300 K (Fig. 2(a)). It can be fitted very well using the Curie–Weiss law , where C is the Curie constant and θ is the Weiss temperature. The linear fit of between 100 K and 300 K with ZFC mode (orange solid line in Fig. 2(a)) gives and K, indicating the dominant AFM interaction in this material. It is also in agreement with the AFM ordering below T_N. The value of C corresponds to the effective moment /Fe, close to the expected local moment of high-spin Fe³⁺ ion (S = 5/2, spin-only /Fe). Compared to isostructural Ba₂BiFeSe₅ with larger K, the shortest Fe–Fe distance in Ba₂BiFeS₅ (5.864 Å) is shorter than that in Ba₂BiFeSe₅ (6.0 Å),^[21] indicating the direct magnetic interactions may not be dominant. Meanwhile, band structure calculations show that Ba₂BiFeS₅ is an insulator with no conduction electron,^[19] so that the RKKY interaction is excluded. Thus one of the possible magnetic interacting mechanisms is superexchanging interaction, i.e., Fe atoms interact with each other via Bi and/or S atoms.^[21] Figure 2(b) shows the field dependence of magnetization M(H) at various temperatures. The loops exhibit the almost linear behaviors without the trend of saturation, irrespective of temperatures, consistent with the feature of AFM transition in Ba₂BiFeS₅. It has to be noted that there is a small hysteresis at low-field region for all of curves, even when . This could originate from the minor ferromagnetic impurities in the sample.

Fig. 2.

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Fig. 2. (a) Temperature dependence of magnetization M(T) from 1.8 K to 300 K with the zero-field cooling (ZFC) and the field cooling (FC) modes and the Curie–Weiss fitting of temperature dependence of inverse magnetic susceptibility 1/χ(T) (orange solid line). Inset: as a function of T. (b) Isothermal magnetization hysteresis loops in the field range from −5 T to 5 T at various temperatures. Inset: the enlarged part of curves at low-field region.

The specific heat capacity C_p(T) measurement from 2 K to 150 K is presented in Fig. 3(a). An anomalous behavior can be obviously observed at 31.3 K, corresponding to the long-range AFM transition. The T_N obtained from the peak in C_p(T) curve is close to that derived from the curve in the inset of Fig. 2(a). Because of the AFM insulator feature of Ba₂BiFeS₅,^[19] the total specific heat capacity can be divided into lattice (C_ph) and magnetic (C_m) parts. The C_ph can be fitted using the 5th polynomial between temperature range of 2 K–10 K and 70 K–100 K (red solid line in Fig. 3(a)). This method has been adopted in previous reports to estimate the heat capacity of lattice vibration.^[25–27] After subtracting the lattice contribution, the obtained C_m(T) is presented in Fig. 3(b) (green symbols). There is a peak shown in C_m(T) curve, corresponding to the paramagnetic (PM) to AFM transition.

Fig. 3.

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Fig. 3. (a) Temperature dependence of heat capacity Cp(T) for Ba2BiFeS5 single crystal at zero field. The red solid curve represents the lattice contribution, fitted by a polynomial. Inset: enlarged part at low temperature region. The red solid line is the fit using the formula . (b) Temperature dependence of Cm(T) (left label, green symbols) and Sm(T) curves (right label, orange solid line). The brown dashed line represents the theoretical value of Sm ( for S = 5/2 system).

Magnetic entropy S_m(T) can be calculated by integrating the C_m/T. The derived temperature dependence of S_m(T) is shown in Fig. 3(b) (orange solid line). It can be seen that the S_m(T) is small when T is far below T_N. However, it increases dramatically when T is approaching T_N because of the significant release of magnetic entropy at PM–AFM traction. Finally, it becomes saturated at higher temperature. The value of S_m at 100 K is , which is much smaller than theoretical value for high-spin Fe³⁺ ion with S = 5/2 (brown dashed line, Fig. 3(b)). One of the possible reasons is the existing of short range magnetic fluctuation above T_N, partially reflecting from the difference between the θ and T_N. The overestimation of C_ph would be another reason causing the smaller values of C_m and corresponding S_m than actual ones. On the other hand, assuming the neglible contribution of C_m(T) at low temperature ( K), the C_p(T) can be well fitted using the formula (inset of Fig. 3(a)). The value of coefficient related to the phonon contribution β is 4.85(9) and the calculated Debye temperature is K using the formula , where N is the atomic number in the chemical formula (N = 9) and R is the gas constant ( ). It should be noted that the derived from fitted β has some uncertainty because the temperature dependence of heat capacity for antiferromagnetic magnons excitation also follow the behavior.

In summary, we grew single crystal of Ba₂BiFeS₅ containing 0D structural unit of FeS₄ tetrahedra. The fit of high-temperature M(T) curve using the Curie–Weiss law gives the /Fe, indicating that the Fe³⁺ ions in this compound are at the high-spin state ( ). Moreover, the negative value of θ ( K) suggests the dominant AFM interaction. The long-range AFM order forms at 30 K, confirmed by both magnetization and heat capacity measurements. By analyzing the C_m(T), we find that the S_m at T_N ( K⁻¹) is much smaller than the theoretical value for high-spin state Fe³⁺ ions ( ). It might be ascribed to the short-range antiferromagnetic fluctuation above T_N or the overestimated phonon contribution to heat capacity.