Coexistence of superconductivity and ferromagnetism in Sr0.5Ce0.5FBiS2-xSex (x = 0.5 and 1.0), a non-U material with Tc < TFM

We have carried out detailed magnetic and transport studies of the new Sr0.5Ce0.5FBiS2-xSex (0.0 ≤ x ≤ 1.0) superconductors derived by doping Se in Sr0.5Ce0.5FBiS2. Se–doping produces several effects: it suppresses semiconducting–like behavior observed in the undoped Sr0.5Ce0.5FBiS2, the ferromagnetic ordering temperature, TFM, decreases considerably from 7.5 K (in Sr0.5Ce0.5FBiS2) to 3.5 K and the superconducting transition temperature, Tc, gets enhanced slightly to 2.9–3.3 K. Thus in these Se–doped materials, TFM is marginally higher than Tc. Magnetization studies provide evidence of bulk superconductivity in Sr0.5Ce0.5FBiS2-xSex at x ≥ 0.5 in contrast to the undoped Sr0.5Ce0.5FBiS2 (x = 0) where magnetization measurements indicate a small superconducting volume fraction. Quite remarkably, as compared with the effective paramagnetic Ce–moment (~2.2 μB), the ferromagnetically ordered Ce–moment in the superconducting state is rather small (~0.1 μB) suggesting itinerant ferromagnetism. To the best of our knowledge, Sr0.5Ce0.5FBiS2-x Sex (x = 0.5 and 1.0) are distinctive Ce–based bulk superconducting itinerant ferromagnetic materials with Tc < TFM. Furthermore, a novel feature of these materials is that they exhibit a dual and quite unusual hysteresis loop corresponding to both the ferromagnetism and the coexisting bulk superconductivity.

to exhibit superconductivity [19][20][21][22][23][24][25] . SrFBiS 2 is derived by replacing Ln-O layers by Sr-F layers. Its structure essentially consists of alternate stacking of conducting BiS 2 layers and blocking (insulating) layer LnO/SrF 15,17,19 . Electron carriers are doped into the superconducting BiS 2 layers employing the commonly used doping strategy, namely, replacing O partially by F, for instance LaO 0.5 F 0.5 BiS 2 exhibits superconductivity at T c ~ 2.8 K 19 . In AFBiS 2 electron doping and eventual superconductivity is achieved/enhanced by Ln (La and Ce) doping at A sites [26][27][28][29] . Structurally, these materials are quite similar to high-T c cuprates and iron pnictides and superconductivity is quite robust as evident from numerous studies on various site substitutions 24,[30][31][32] . T c is enhanced in LnO 1-x F x BiS 2 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] . YbO 0.5 F 0.5 BiS 2 has the highest T c = 5.4 K among LnO 1-x F x BiS 2 and, interestingly, it undergoes an antiferromagnetic transition (T N ~ 2.7 K) also 23 . Se substitution has been realized in LaO 0.5 F 0.5 BiS 2-x Se x 37 where an enhancement of T c is observed with maximum T c of 3.8 K for LaO 0.5 F 0.5 BiSSe composition (x = 1.0). T c decreases on further Se substitution. For other rare earths (Ce and Nd), however, the effect of Se on T c is different. In Ce(O/F)BiS 2 enhancement in T c is only marginal (2.4 to 2.6 K) 38 . Se substitution induces bulk superconductivity in La and Ce materials. In Nd(O/F)BiS 2 and Bi 4 O 4 S 3 , Se doping has been shown to depress T c 32,39 . Se substitution in AFBiS 2 has not been tried so far. Under applied pressure, T c is enhanced in LnO 1-x F x BiS 2 and A 1-x Ln x FBiS 2 (Ln = La, Ce, Pr and Nd; A = Sr and Eu) upto a maximum of 10 K [40][41][42][43][44][45][46] . The Bi-S 2 materials are BCS-like and probably have s-wave pairing symmetry [47][48][49][50][51] . But there is yet no consensus on the origin of superconductivity in these materials 31 .
Very recently, ferromagnetism and superconductivity have been reported to coexist in CeO 1-x F x BiS 2 and Sr 1-x Ce x FBiS 2 with T c ~ 2.5-4 K and T FM ~4-8 K 20,27,52-54 . As these materials have layered structure, magnetism originates in the Ce− O (or Sr/Ce− F) layers and conduction occurs in BiS 2 layers. In Sr 0.5 Ce 0.5 FBiS 2 , the parent materials for our Se-added materials Sr 0.5 Ce 0.5 FBiS 2-x Se x , Ce-substitution provides conduction electrons as well as gives rise to long range magnetic order 27 . 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 Sr 0.5 Ce 0.5 FBiS 2 . Se-doping leads to a modest enhancement of T c (upto 3.3 K) and a significant depression of T FM (down to 3.5 K). Thus Se-doping moves T c and T FM in opposite directions, bringing them in closer proximity in temperature. We believe the ferromagnetism in our materials is itinerant just as it is in UCoGe 13 , namely, high Ce-paramagnetic moment (~2.2 μ B ) and small saturation Ce-magnetic moment (0.1 μ B ). To the best of our knowledge, the materials Sr 0.5 Ce 0.5 FBiS 2-x Se x , 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 Sr 0.5 Ce 0.5 FBiS 2-x Se x is a timely discovery, in that it puts U-and Ce on equal footing in this respect also.  Fig. 1. All the peaks could be easily indexed on the basis of a SrFBiS 2 type tetragonal unit cell (SG: P4/nmm). Minor peaks corresponding to the impurity of Bi 2 S 3 (#) and Bi 2 Se 3 (*) were also observed for composition with x > 0. The estimated impurity phase of Bi 2 S 3 was ~4% observed in x = 0.3 composition whereas the amount of Bi 2 Se 3 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 Bi 2 Se 3 , which is non-magnetic and insulating under ambient pressure 55 . It does not interfere with superconducting and magnetic properties of the materials under investigation. Resistivity. Resistivity of the materials as a function of temperature is shown in Fig. 2. In the normal state, resistivity of Sr 0.5 Ce 0.5 FBiS 2-x Se x 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 T c = 2.9 and 3.3 K in materials with x = 0.5 and 1.0 respectively. Our estimate of T c onset is based on a 90% criterion as shown in Fig. 2(b). Se-doping clearly enhances T c 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 Δ T = 0.2 K. Similar small enhancement in T c with Se substitution was previously observed in LnO 1-x F x BiS 2 (Ln = La and Ce) 38,56,57 . This enhancement in T c 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, B c2 (T) as a function of temperature is given in the inset of Fig. 2(a). We estimated B c2 below 2 K using a standard single-band Werthamer-Helfand-Hohenberg (WHH) formula with the Maki parameter 59 α = 0. Upper critical field, B c2 (0) at T = 0 is estimated to be 2.6 T for x = 0.5 and 3.3 T for x = 1.0. These B c2 values are atleast twice higher than those reported for the Se-free samples Sr 0.5 Ln 0.5 FBiS 2 26,27 . Enhancement of T c and B c2 in the Se-doped samples clearly indicates that Se atoms have entered the lattice. Enhancement of B c2 implies reduction of the coherence length or stronger impurity scattering due to Se doping in Sr 0.5 Ce 0.5 FBiS 2 .

Results and Discussion
Magnetic susceptibility in low field of 10 Oe. Figure 3(a) shows dc susceptibility of Sr 0.5 Ce 0.5 FBiS 2-x Se x (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 studies 60-65 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 Sr 0.5 Ce 0.5 FBiS 2 (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 T c onset = 2.65 K for x = 0.5 to T c onset = 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 Sr 0.5 Ce 0.5 FBiS 2 27,44 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 T FM = 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.
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. T c and T FM 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 T c in Sr 0.5 Ce 0.5 FBiS 2-x Se x .

High field DC magnetization measurements. Magnetic susceptibility χ(T), measured in an applied
field of 10 kOe, and its inverse in Sr 0.5 Ce 0.5 FBiS 2-x Se x (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) = χ o + C/(T− θ ), the paramagnetic effective magnetic moments obtained for the two samples are: μ eff = 2.22 μ B for x = 0.5 and 2.29μ B for x = 1.0 (see Figure S3 in SM). These values are close to the theoretical value 2.54 μ B for free Ce 3+ 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 Sr 0.5 Ce 0.5 FBiS 1.5 Se 0.5 and Sr 0.5 Ce 0.5 FBiSSe. 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 (T c < T < T FM ) but no superconducting hysteresis loop as such was observed 66 . 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 H c1 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 Sr 0.5 Ce 0.5 FBiS 2 (T c ~ 2.6 K &T FM ~ 7.5 K) 27,44 and in a similar material Ce(O, F)BiS 2 (T c ~ 2.5-4 K & T FM ~ 6.5-7.5 K) 20,52,53,67 no superconducting hysteresis loop was observed. This is consistent with our own results on Sr 0.5 Ce 0.5 FBiS 2 (inset of Fig. 4a). Thus Se-doping has created crucial changes in the superconducting and magnetic properties of the parent material Sr 0.5 Ce 0.5 FBiS 2 . Observation of superconducting loop is a good indication of bulk superconductivity.
Dual hysteresis loop has been observed very recently in [(Li 1-x Fe x )OH](Fe 1-y Li y )Se 68 . However, there is a fundamental difference in this material and our samples, namely, in this case, T c (~43 K) > > T FM (10 K) whereas in our case T c < T FM and hence, superconductivity sets in an already ferromagnetically ordered lattice. Further, in our case, superconductivity appears just at the border of ferromagnetic transition (T FM is only marginally higher than T c ) whereas in the above-mentioned material, superconductivity and ferromagnetism are far separated in temperature. In CeFeAs 1-x P x O 0.95 F 0.05 , coexistence of superconductivity and ferromagnetism (with T c > T FM ) has been observed 69 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 M s is estimated by linear extrapolation of the high-field data to H = 0 ( Fig. 4(a) and (c)). From the estimated M s , we obtain at T = 2 K, the spontaneous Ce-moment μ 0 ~ 0.09 μ B for the sample x = 0.5 and 0.11 μ B for the sample x = 1.0. These values are quite small as compared with what is expected for free Ce 3+ ion. We may note here that in Ce(O, F)BiS 2 a reduced moment M s = 0.52 μ B /Ce was reported 53 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.  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, H c1 .
Scientific RepoRts | 6:37527 | DOI: 10.1038/srep37527 The transition of the high Ce-paramagnetic effective moment μ eff ~ 2.2 μ B to a small ordered moment μ 0 ~ 0.1 μ B 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 μ eff /μ 0 (~22) implies an itinerant ferromagnetic state 13,70 in both materials Sr 0.5 Ce 0.5 FBiS 2-x Se x , 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 Sr 0.5 Ce 0.5 FBiS 1.5 Se 0.5 (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 T FM ~ 3.6 K is obtained. As T FM and T c 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 CeO 0.5 F 0.5 BiS 2 and YbO 0.5 F 0.5 BiS 2 specific heat anomaly around T c is not observed 23 27 . However, it is larger by a factor of 5-10 as compared to Sr 1-x La x FBiS 2 (γ < 2 mJ/mol-K 2 ) 26,71,72 and La 1−x M x OBiS 2 (M = Ti, Zr, Th) (γ ∼ 0.58-2.21 mJ/mol K 2 ) 24 . Ce 4f-electrons are responsible for the increased density of states at the Fermi level in Sr 0.5 Ce 0.5 FBiS 1.5 Se 0.5 as compared to that in other BiS 2 system without Ce. Therefore, the higher γ value in the normal state of Sr 0.5 Ce 0.5 FBiS 2 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 (S m = 0.04Rln6) is consistent with weak itinerant ferromagnetism in Sr 0.5 Ce 0.5 FBiS 1.5 Se 0.5 . This situation is similar to that in UCoGe 13 .
With the help of our experimental data, we construct a ferromagnetism/superconductivity phase diagram of the system Sr 0.5 Ce 0.5 FBiS 2-x Se x (0 ≤ x ≤ 1) which is shown in Fig. 6. Upon doping Se ferromagnetic ordering temperature (T FM ) decrease along with a concomitant increase in the T c . 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. T FM and T c lie in close proximity in the x = 1.0 composition.
After submission of this manuscript we came across a report on the coexistense of superconductivity and ferromagnetism in CsEuFe 4 As 4 compound 73 . 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 (T c ~ 3.0 K) and itinerant ferromagnetism (T FM ~ 3.5 K) coexisting in the new materials Sr 0.5 Ce 0.5 FBiS 2-x Se x 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 Sr 0.5 Ce 0.5 FBiS 2-x Se x is an important and timely addition to the exciting Ce-based materials exhibiting coexisting superconductivity and magnetism. The materials Sr 0.5 Ce 0.5 FBiS 2-x Se x are potential candidates for the unconventional p-wave superconductivity 74 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 Sr 0.5 Ce 0.5 FBiS 2-x Se x (x = 0.0, 0.3, 0.5 and 1.0) were prepared by the usual solid state synthesis procedure as reported elsewhere 28,35 . SrF 2 , Bi and Se powder, pre-reacted Ce 2 S 3 and Bi 2 S 3 powder were thoroughly mixed, pelletized and sealed in quartz tube under vacuum. The tubes were then heated twice at 800 o C 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.