Introduction

Traditionally, superconductivity and long–range ferromagnetism had been considered mutually exclusive (BCS pair–breaking and Meissner effect). For example, in several ternary materials RMo6X8 (X = S, Se)1 and RRh4B42,3, studied in the early eighties, superconductivity was observed coexisting with long range antiferromagnetic order. But uniform ferromagnetism suppressed superconductivity at low temperatures4,5,6. The situation has changed strikingly over the last several years with the discovery of a number of materials that do exhibit coexistence of superconductivity and long-range ferromagnetism. In materials such as ErNi2B2C7,8 and RuSr2GdCu2O89, localized 4f–moments (Er, Gd) are responsible for long-range ferromagnetism whereas 3d–conduction electrons carry superconductivity. In certain U-containing materials, such as UGe210, URhGe11, UIr12, UCoGe13, the situation is drastically different. Here U–5f itinerant electrons are responsible for both superconductivity and ferromagnetism. These materials, with TFM > TSC, present an unusual and surprising scenario of coexistence, namely, superconductivity setting in an already ferromagnetically ordered host. In such cases, spin-triplet pairing (p-wave superconductivity) has been suggested (U-compounds such as UCoGe, URhGe and UGe2 have been proposed/considered p-wave ferromagnetic superconductors)14 to be compatible with itinerant ferromagnetism. For p-wave pairing, one needs to go beyond electron-phonon interaction (pairing mechanism in conventional superconductivity) with Cooper-pairing mediated via spin fluctuations. The material UCoGe is of particular interest from the viewpoint of the present work. In this material the paramagnetic effective moment of U is ~1.7 μB whereas the ferromagnetic ordered moment of U is drastically reduced, 0.03 μB13. The materials under investigation (the title compounds) in this work, exhibit coexisting superconductivity and itinerant ferromagnetic properties, as we shall see below, similar to those of UCoGe.

The parent material Sr0.5Ce0.5FBiS2 of the title compounds Sr0.5Ce0.5FBiS2-xSex belongs to a small class AFBiS2 (A = Sr and Eu)15,16 of a larger family of BiS2 layered tetragonal materials LnOBiS217,18 (P4/nmm) recently shown to exhibit superconductivity19,20,21,22,23,24,25. SrFBiS2 is derived by replacing Ln–O layers by Sr–F layers. Its structure essentially consists of alternate stacking of conducting BiS2 layers and blocking (insulating) layer LnO/SrF15,17,19. Electron carriers are doped into the superconducting BiS2 layers employing the commonly used doping strategy, namely, replacing O partially by F, for instance LaO0.5F0.5BiS2 exhibits superconductivity at Tc ~ 2.8 K19. In AFBiS2 electron doping and eventual superconductivity is achieved/enhanced by Ln (La and Ce) doping at A sites26,27,28,29. Structurally, these materials are quite similar to high-Tc cuprates and iron pnictides and superconductivity is quite robust as evident from numerous studies on various site substitutions24,30,31,32. Tc is enhanced in LnO1-xFxBiS2 by chemical pressure via partial or complete substitution of La by a smaller rare-earth (Ln = Ce, Pr, Nd, Sm and Yb)23,33,34,35,36. YbO0.5F0.5BiS2 has the highest Tc = 5.4 K among LnO1-xFxBiS2 and, interestingly, it undergoes an antiferromagnetic transition (TN ~ 2.7 K) also23. Se substitution has been realized in LaO0.5F0.5BiS2-xSex37 where an enhancement of Tc is observed with maximum Tc of 3.8 K for LaO0.5F0.5BiSSe composition (x = 1.0). Tc decreases on further Se substitution. For other rare earths (Ce and Nd), however, the effect of Se on Tc is different. In Ce(O/F)BiS2 enhancement in Tc is only marginal (2.4 to 2.6 K)38. Se substitution induces bulk superconductivity in La and Ce materials. In Nd(O/F)BiS2 and Bi4O4S3, Se doping has been shown to depress Tc32,39. Se substitution in AFBiS2 has not been tried so far. Under applied pressure, Tc is enhanced in LnO1-xFxBiS2 and A1-xLnxFBiS2 (Ln = La, Ce, Pr and Nd; A = Sr and Eu) upto a maximum of 10 K40,41,42,43,44,45,46. The Bi-S2 materials are BCS-like and probably have s-wave pairing symmetry47,48,49,50,51. But there is yet no consensus on the origin of superconductivity in these materials31.

Very recently, ferromagnetism and superconductivity have been reported to coexist in CeO1-x FxBiS2 and Sr1-xCexFBiS2 with Tc ~ 2.5–4 K and TFM ~4–8 K20,27,52,53,54. As these materials have layered structure, magnetism originates in the Ce−O (or Sr/Ce−F) layers and conduction occurs in BiS2 layers. In Sr0.5Ce0.5FBiS2, the parent materials for our Se–added materials Sr0.5Ce0.5FBiS2-xSex, Ce–substitution provides conduction electrons as well as gives rise to long range magnetic order27. Ferromagnetic order takes place at a higher temperature (7.5 K) and superconductivity sets in at a lower temperature (2.8 K) in an already ferromagnetically ordered lattice. We report here the effect of substitution of larger isovalent Se ion at the S site on the magnetic and superconducting properties of Sr0.5Ce0.5FBiS2. Se–doping leads to a modest enhancement of Tc (upto 3.3 K) and a significant depression of TFM (down to 3.5 K). Thus Se–doping moves Tc and TFM in opposite directions, bringing them in closer proximity in temperature. We believe the ferromagnetism in our materials is itinerant just as it is in UCoGe13, namely, high Ce-paramagnetic moment (~2.2 μB) and small saturation Ce-magnetic moment (0.1 μB). To the best of our knowledge, the materials Sr0.5Ce0.5FBiS2-xSex, x = 0.5, 1.0 are unique Ce-containing materials exhibiting coexisting bulk superconductivity and itinerant ferromagnetism. Thus our observation of the coexistence of superconductivity and itinerant ferromagnetism in Sr0.5Ce0.5FBiS2-xSex is a timely discovery, in that it puts U- and Ce on equal footing in this respect also.

Results and Discussion

PXRD characterization

PXRD patterns of all the Sr0.5Ce0.5FBiS2-xSex (x = 0.0, 0.3, 0.5 and 1.0) compositions are shown in Fig. 1. All the peaks could be easily indexed on the basis of a SrFBiS2 type tetragonal unit cell (SG: P4/nmm). Minor peaks corresponding to the impurity of Bi2S3 (#) and Bi2Se3 (*) were also observed for composition with x > 0. The estimated impurity phase of Bi2S3 was ~4% observed in x = 0.3 composition whereas the amount of Bi2Se3 was ~6% and ~14% in x = 0.5 and x = 1.0 composition respectively. It is evident from X-ray studies that the impurities increase with the increase of Se content. The samples with x > 1.0 were obtained as multiphase products. This indicates a Se solubility limit of x ~ 1.0. Lattice parameters a and c show an expected increase upon Se doping (a = 4.0886(2) Å, c = 13.4143(8) Å for x = 0.5 and a = 4.1057(1) Å, c = 13.4756(8) Å for x = 1.0) resulting in the monotonous unit cell expansion (inset in Fig. 1). Compositional analysis on x = 0.5 and 1.0 samples gives a stoichiometry close to the nominal value for both the compositions (Figure S1 in supplementary material (SM)). For x = 1.0 sample, the Se:S ratio was slightly less than 1, possibly due to the formation of small amount of the impurity phase Bi2Se3, which is non-magnetic and insulating under ambient pressure55. It does not interfere with superconducting and magnetic properties of the materials under investigation.

Figure 1
figure 1

Powder X-ray diffraction of Sr0.5Ce0.5FBiS2-xSex(x = 0.0, 0.3, 0.5 and 1.0). Symbols (*) and (#) indicate impurity phases Bi2Se3 and Bi2S3 respectively. Inset shows the variation of cell volume with Se content.

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Resistivity

Resistivity of the materials as a function of temperature is shown in Fig. 2. In the normal state, resistivity of Sr0.5Ce0.5FBiS2-xSex with x = 0 and 0.3 exhibit semiconducting–like temperature dependence, namely, it increases with the decrease of temperature just before the onset of superconducting transition at 2.4 K and 2.7 K respectively as shown in Fig. 2(a). Note that the resistivity values for x = 0 and 0.3 were divided by a factor of 20 and 4 respectively for the purpose of clarity. In the higher Se–doped materials, x = 0.5 and x = 1.0, this semiconducting behavior is progressively subdued and metallic conductivity is observed in the normal state. Superconductivity sets in at Tc = 2.9 and 3.3 K in materials with x = 0.5 and 1.0 respectively. Our estimate of Tconset is based on a 90% criterion as shown in Fig. 2(b). Se–doping clearly enhances Tc by ~1 K (inset of Fig. 2(b)). In the material with x = 1.0, a sharp superconducting transition is observed with a transition width ΔT = 0.2 K. Similar small enhancement in Tc with Se substitution was previously observed in LnO1-xFxBiS2 (Ln = La and Ce)38,56,57. This enhancement in Tc is attributed to the in-plane chemical pressure induced by the Se substitution at S sites as elucidated by Mizuguchi et al.58. The plot of upper critical field, Bc2 (T) as a function of temperature is given in the inset of Fig. 2(a). We estimated Bc2 below 2 K using a standard single-band Werthamer–Helfand–Hohenberg (WHH) formula with the Maki parameter59 α = 0. Upper critical field, Bc2(0) at T = 0 is estimated to be 2.6 T for x = 0.5 and 3.3 T for x = 1.0. These Bc2 values are atleast twice higher than those reported for the Se–free samples Sr0.5Ln0.5FBiS226,27. Enhancement of Tc and Bc2 in the Se–doped samples clearly indicates that Se atoms have entered the lattice. Enhancement of Bc2 implies reduction of the coherence length or stronger impurity scattering due to Se doping in Sr0.5Ce0.5FBiS2.

Figure 2
figure 2

Variable temperature resistivity curves for Sr0.5Ce0.5FBiS2-xSex; x = 0, 0.3, 0.5 and 1.0. The data for x = 0 and 0.3 have been divided by 20 and 4 respectively (a) in temperature range 2–300 K and (b) in low temperature range. Inset of (a) shows the upper critical field (Bc2) versus temperature (T) curve for the x = 0.5 and 1.0 compositions (open circles) along with the WHH fit (solid lines). Inset of (b) shows the variation of Tconset and Tc (ρ = zero) as a function of Se-doping.

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Magnetic susceptibility in low field of 10 Oe

Figure 3(a) shows dc susceptibility of Sr0.5Ce0.5FBiS2-xSex (x = 0.5 and 1.0), in both the field-cooled (FC) and the zero field-cooled (ZFC) conditions in an applied field of 10 Oe. Clear diamagnetic signal, of magnitude close to the theoretical value, for both the x = 0.5 and 1.0 compositions is observed in ZFC condition (Fig. 3a) establishing the superconducting state. Poor Meissner response in both cases is possibly due to flux pinning. A superconducting volume fraction of >95% is estimated for both x = 0.5 and 1.0 compositions. In several studies60,61,62,63,64,65 on a variety of materials, such large diamagnetic superconducting signals have been observed and have been considered suggesting bulk superconductivity therein. Inset of Fig. 3(a) shows dc susceptibility of the Se free sample Sr0.5Ce0.5FBiS2 (x = 0.0) which shows a ferromagnetic behavior with Curie temperature ~7.5 K, similar to that reported earlier by Li et al.27. A weak drop in the ZFC susceptibility below 3 K is due to the superconducting transition that was also observed in our resistivity measurements. Such a weak diamagnetic signal rules out bulk superconductivity in parent sample x = 0.0 and is consistent with weak superconductivity. Figure 3(b) shows both the real and the imaginary parts of the ac susceptibility. A large superconducting screening indicates bulk superconductivity. Moreover a larger imaginary part of the signal indicates a considerable energy loss due to movement of vortices. Such a behavior cannot be explained if superconductivity is present only in thin surface layers. As deduced from these measurements, superconducting transition temperature increases from Tconset = 2.65 K for x = 0.5 to Tconset = 3.20 K for x = 1 which corroborates well with the resistivity data described above. It must be pointed out that in the earlier measurements on Se–free Sr0.5Ce0.5FBiS227,44 materials diamagnetic signal was not observed and the occurrence of superconductivity was inferred from the resistivity measurements only. Inset of Fig. 3b shows the low temperature ac susceptibility (real part) data for the compositions with x = 0.3 in comparison with x = 0.5 and 1.0 samples. It shows a ferromagnetic behavior similar to x = 0.0 with a reduced Curie temperature TFM = 4.1 K. No diamagnetic signal was observed indicating that similar to the parent compound x = 0.3 is also a weak superconductor. A clear diamagnetic signal is observed only for x = 0.5 and 1.0 samples.

Figure 3
figure 3

(a) Variable temperature dc susceptibility in ZFC and FC protocols for Sr0.5Ce0.5FBiS2-xSex (x = 0.5, 1.0) in an applied field of 10 Oe. Inset shows dc susceptibility for x = 0.0 sample in comparison with x = 0.5 sample in the same units (emu/mol) and (b) Real and imaginary parts of ac susceptibility for x = 0.5 and 1.0 samples. Inset shows ac susceptibility for x = 0.3 sample in comparison with x = 0.5 and 1.0 samples.

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Further, in Fig. 3(a), a weak magnetic anomaly is discernible at 3.5 K for the sample x = 0.5 which corresponds to a ferromagnetic transition as evidenced in our high field measurements, (see below), for both the samples x = 0.5 and x = 1.0. This anomaly is not observed clearly for the sample x = 1.0. Tc and TFM were ascertained from the derivative plots of susceptibility (see Figure S2 in SM). It is evident from the susceptibility studies that Se substitution depresses ferromagnetic ordering and enhances Tc in Sr0.5Ce0.5FBiS2-xSex.

High field DC magnetization measurements

Magnetic susceptibility χ(T), measured in an applied field of 10 kOe, and its inverse in Sr0.5Ce0.5FBiS2-xSex (x = 0.5 and 1.0) is presented in the Figure S3 in SM. By fitting the data above 50 K to the Curie–Weiss law χ(T) = χo + C/(T−θ), the paramagnetic effective magnetic moments obtained for the two samples are: μeff = 2.22 μB for x = 0.5 and 2.29μB for x = 1.0 (see Figure S3 in SM). These values are close to the theoretical value 2.54 μB for free Ce3+ ions. Thus Ce–ions are in trivalent (or nearly trivalent state) state.

We display in Fig. 4 the results of our magnetization measurements, at a few selected temperatures 5 K, 3.5 K and 2 K, in Sr0.5Ce0.5FBiS1.5Se0.5 and Sr0.5Ce0.5FBiSSe. At 5 K, magnetization M varies linearly with applied magnetic field, suggesting a paramagnetic state (no magnetic order). At 3.5 K, M is no longer linear in H in the low field region and shows a sign of a ferromagnetic behavior. Ferromagnetic state is clearly observed at a lower temperature 2 K and, remarkably, at this temperature in both the samples, we observe a ferromagnetic hysteresis loop and a superimposed superconducting hysteresis loop, demonstrating unambiguously the coexistence of ferromagnetism and bulk superconductivity. A dual loop, displaying the two ordered states, superconductivity and ferromagnetism, with such clarity, is a novel feature of this material. In UCoGe, ferromagnetic hysteresis is observed in the ferromagnetic state (Tc < T < TFM) but no superconducting hysteresis loop as such was observed66. Inset of Fig. 4a shows the isothermal magnetization (at 2 K) for x = 0.0 where only a ferromagnetic hysteresis loop is observed. In the inset of Fig. 4(b) and (d) the diamagnetic response is clearly seen in the virgin low field region (from which Hc1 is easily estimated to be ~44 Oe and 40 Oe for x = 0.5 and 1.0 respectively. It is important to point out that in the selenium-free compound Sr0.5Ce0.5FBiS2 (Tc ~ 2.6 K &TFM ~ 7.5 K)27,44 and in a similar material Ce(O, F)BiS2 (Tc ~ 2.5–4 K & TFM ~ 6.5–7.5 K)20,52,53,67 no superconducting hysteresis loop was observed. This is consistent with our own results on Sr0.5Ce0.5FBiS2 (inset of Fig. 4a). Thus Se–doping has created crucial changes in the superconducting and magnetic properties of the parent material Sr0.5Ce0.5FBiS2. Observation of superconducting loop is a good indication of bulk superconductivity.

Figure 4
figure 4

Hysteresis loops at different temperatures for Sr0.5Ce0.5FBiS1.5Se0.5 and Sr0.5Ce0.5FBiSSe in H ≤ 10 kOe (a) and (c) and H ≤ 1.5 kOe (b) and (d). The superconducting loop is superimposed on the ferromagnetic loop at 2 K. Inset in Fig. 4(a) shows the ferromagnetic hysteresis loop for x = 0 composition. Insets in Fig. 4(b) and (d) show initial diamagnetic signal with arrows indicating lower critical field, Hc1.

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Dual hysteresis loop has been observed very recently in [(Li1-xFex)OH](Fe1-yLiy)Se68. However, there is a fundamental difference in this material and our samples, namely, in this case, Tc (~43 K) >>TFM (10 K) whereas in our case Tc < TFM and hence, superconductivity sets in an already ferromagnetically ordered lattice. Further, in our case, superconductivity appears just at the border of ferromagnetic transition (TFM is only marginally higher than Tc) whereas in the above–mentioned material, superconductivity and ferromagnetism are far separated in temperature. In CeFeAs1-xPxO0.95F0.05, coexistence of superconductivity and ferromagnetism (with Tc > TFM) has been observed69 in a limited doping range. In this case, however, Ce carries almost full moment and the system is not an itinerant ferromagnet.

The spontaneous magnetization Ms is estimated by linear extrapolation of the high–field data to H = 0 (Fig. 4(a) and (c)). From the estimated Ms, we obtain at T = 2 K, the spontaneous Ce–moment μ0 ~ 0.09 μB for the sample x = 0.5 and 0.11 μB for the sample x = 1.0. These values are quite small as compared with what is expected for free Ce3+ ion. We may note here that in Ce(O, F)BiS2 a reduced moment Ms = 0.52 μB/Ce was reported53 which, possibly, suggests that in this case Ce–ions may be in the crystal–field split doublet state (localized moment). In our case, we observe a drastically reduced, but non–zero, Ce–moment.

The transition of the high Ce–paramagnetic effective moment μeff ~ 2.2 μB to a small ordered moment μ0 ~ 0.1 μB in the superconducting state is an important observation as the drastic loss of Ce–moment signals a delocalization of the 4f electrons concurrent with the appearance of superconductivity. Thus, 4f–electrons may also be involved in superconductivity in these materials. A high ratio μeff/μ0 (~22) implies an itinerant ferromagnetic state13,70 in both materials Sr0.5Ce0.5FBiS2-xSex, x = 0.5 and x = 1.0. Further, as Ce–atoms are responsible both for ferromagnetism and coexisting bulk superconductivity we think the two phenomena can coexist uniformly. These materials fill the glaring void, namely, so far no Ce–based material has been hitherto known exhibiting superconductivity within the itinerant ferromagnetic state.

Specific heat

Figure 5 shows the temperature dependence of specific heat of Sr0.5Ce0.5FBiS1.5Se0.5 (x = 0.5) in the low temperature range 2–16 K. Inset shows C/T data before (blue circle) and after subtraction (black circle) of a Schottky contribution which was approximated by the dashed line. A broad peak, not λ–shaped as expected for a ferromagnet, centered at 3.2 K (inset of Fig. 5) is observed from which, following Li et al.27, ferromagnetic ordering temperature TFM ~ 3.6 K is obtained. As TFM and Tc are quite close, separate anomalies of the two transitions, the magnetic and the superconducting, are not resolved. It should be pointed that in similar systems like CeO0.5F0.5BiS2 and YbO0.5F0.5BiS2 specific heat anomaly around Tc is not observed23 and the anomaly observed in Sr0.5Ce0.5FBiS2 is extremely small53. Red line in the main panel of Fig. 5 obeys the equation: C/T = γ + βT 2 yielding the Debye temperature θD = 187 K and the Sommerfeld coefficient γ = 12 mJ/(K2mol Ce). This γ value of Sr0.5Ce0.5FBiS1.5Se0.5 is much smaller than that of Sr0.5Ce0.5FBiS2 (γ = 117 mJ/(K2mol Ce))27. However, it is larger by a factor of 5–10 as compared to Sr1-xLaxFBiS2 (γ < 2 mJ/mol-K2)26,71,72 and La1−xMxOBiS2 (M = Ti, Zr, Th) (γ ∼ 0.58–2.21 mJ/mol K2)24. Ce 4f–electrons are responsible for the increased density of states at the Fermi level in Sr0.5Ce0.5FBiS1.5Se0.5 as compared to that in other BiS2 system without Ce. Therefore, the higher γ value in the normal state of Sr0.5Ce0.5FBiS2 is attributed to the electronic correlation effect of Ce–4f electrons which are reduced in the Se–doped sample. From the specific heat measurements we get an entropy per Ce atom of only about 4% of the expected value for J = 5/2. The low magnetic entropy (Sm = 0.04Rln6) is consistent with weak itinerant ferromagnetism in Sr0.5Ce0.5FBiS1.5Se0.5. This situation is similar to that in UCoGe13.

Figure 5
figure 5

Temperature dependence of Schottky corrected specific heat C/T vs.T2 for x = 0.5 sample at H = 0. Red line is the linear fit to the equation C/T = γ + β T2. Inset shows C/T data before (blue circle) and after subtraction (black circle) of a Schottky contribution which is represented by the dashed line.

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With the help of our experimental data, we construct a ferromagnetism/superconductivity phase diagram of the system Sr0.5Ce0.5FBiS2-xSex (0 ≤ x ≤ 1) which is shown in Fig. 6. Upon doping Se ferromagnetic ordering temperature (TFM) decrease along with a concomitant increase in the Tc. Ferromagnetism and weak superconductivity are observed for x < 0.5. In the two materials x = 0.5 and x = 1.0, bulk superconductivity is observed coexisting with ferromagnetism. The dual hysteresis loops, shown in Fig. 4, are observed for these samples. TFM and Tclie in close proximity in the x = 1.0 composition.

Figure 6
figure 6

Ferromagnetism and superconductivity phase diagram of Sr0.5Ce0.5FBiS2-xSex (0 ≤ x ≤ 1).

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After submission of this manuscript we came across a report on the coexistense of superconductivity and ferromagnetism in CsEuFe4As4 compound73. A dual hysteresis loop has been observed in this compound also. The superconducting loop, however, is not so prominent. This remark has been added in the revised version of the manuscript.

Concluding Remarks

We have observed superconductivity (Tc ~ 3.0 K) and itinerant ferromagnetism (TFM ~ 3.5 K) coexisting in the new materials Sr0.5Ce0.5FBiS2-xSex at x ≥ 0.5. Thus in these materials, superconductivity occurs much closer to the border of ferromagnetism than in UCoGe. A novel feature of these materials, as compared with the other ferromagnetic superconductors reported so far, is a dual hysteresis loop corresponding to both the coexisting bulk superconductivity and ferromagnetism. Thus Sr0.5Ce0.5FBiS2-xSex is an important and timely addition to the exciting Ce–based materials exhibiting coexisting superconductivity and magnetism. The materials Sr0.5Ce0.5FBiS2-xSex are potential candidates for the unconventional p–wave superconductivity74 and deserve to be further pursued in this regard. We are making efforts to grow single crystals of these materials. In single crystals (if we succeed to grow) or else in polycrystalline materials, we would carry out studies such as NMR, MuSR, neutron diffraction and Andreev reflection to throw further light on the coexistence of superconductivity and ferromagnetism and nature of the superconducting state (p-wave or s-wave) in these materials.

Methods

Polycrystalline compounds of the series Sr0.5Ce0.5FBiS2-xSex (x = 0.0, 0.3, 0.5 and 1.0) were prepared by the usual solid state synthesis procedure as reported elsewhere28,35. SrF2, Bi and Se powder, pre-reacted Ce2S3 and Bi2S3 powder were thoroughly mixed, pelletized and sealed in quartz tube under vacuum. The tubes were then heated twice at 800 oC for 24 hours with an intermediate grinding. The end products were black/dark grayish in color. Phase purity of all the compositions was checked by powder X–ray diffraction (PXRD) technique using Cu−Kα radiation source. Temperature dependent resistivity, magnetization and specific heat measurements were performed using a 14 T PPMS (Quantum Design). The specific heat was measured using a relaxation technique.

Additional Information

How to cite this article: Thakur, G. S. et al. Coexistence of superconductivity and ferromagnetism in Sr0.5Ce0.5FBiS2-xSex (x = 0.5 and 1.0), a non-U material with Tc < TFM. Sci. Rep. 6, 37527; doi: 10.1038/srep37527 (2016).

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