Coexistence of superconductivity and complex 4 magnetism in EuCeBiSF
EuBiSF is a self-doped superconductor due to the mixed valence of Eu. Here we report that, with the Ce substitution for Eu by 50 at.%, the material exhibits ferromagnetic ordering at 8 K for the Ce-4 moment, superconductivity at 2.2 K in the BiS layers, and possibly antiferromagnetic ordering at 2.1 K for the Eu-4 spins. The Eu valence is essentially divalent with the Ce incorporation. We tentatively interpret the coexistence of ferromagnetism and superconductivity by considering different Bi-6 orbitals that are responsible for superconductivity itself and for mediating the ferromagnetic interaction, respectively. We argue that the antiferromagnetic ordering of the Eu-4 spins is most likely due to a magnetic dipole-dipole interaction.
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pacs:74.70.Dd; 74.62.Dh; 75.30.Cr; 74.25.Dw
The coexistence of superconductivity (SC) and magnetic long-range ordering (LRO) has been a long-standing issue in condensed matter physics[1, 2, 3]. For a complex material containing both conduction electrons and local moments, SC may coexist with antiferromagnetic LRO, because superconducting Cooper pairs, with a typical size (i.e. superconducting coherence length) of hundreds of interatomic distance, ’feel’ null net magnetic field. On the other hand. SC rarely coexists with ferromagnetic LRO because the Cooper pairs’ size is generally less than that of the magnetic domain, and SC is suppressed by the spontaneous magnetization and/or internal exchange field via an electromagnetic mechanism or a paramagnetic effect[5, 6]. Earlier examples of ’magnetic superconductors’ mostly show coexistence of SC and antiferromagnetism (AFM), but SC is suppressed or quenched whenever ferromagnetism (FM) appears[1, 2]. However, the EuFeAs-related systems exceptionally show both SC for the Fe-3 conduction electrons and FM for the Eu-4 local moment[7, 8, 9, 10, 11]. Recent neutron diffraction scattering[12, 13, 14] and resonant magnetic x-ray scattering confirmed Eu-4 FM with an order moment of . The coexistence of FM and SC (hereafter abbreviated as ’FM+SC’) is qualitatively explained in terms of Fe-3 multiband effect, which simultaneously enables SC in the FeAs layers and local-moment FM in the Eu sheets via an effective Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction[3, 8]. The exchange coupling between Fe-3 ( and ) superconducting electrons and the Eu-4 local moment can be very weak, as revealed by a recent time-resolved magneto-optical study. Apart from the Eu-4 FM, it was also reported that the Ce-4 FM could coexist with SC in CeFe(As,P)OF system.
Resembling to the doped EuFeAs systems, the Ce-containing BiS-layer based superconductor is possibly another example that hosts FM+SC[18, 19, 20, 21, 22, 23, 24, 25, 26]. As the first BiS-layer based material synthesized in 1970s, CeBiSO intrinsically shows a semiconducting behaviour[28, 29]. Following the discovery of SC in LaBiSOF, SC at 3 K was realized via the fluorine doping in CeBiSO. The striking feature of the Ce-containing superconductor is the ferromagnetic-like transition at 5 K, which often prevails over the superconducting diamagnetism[18, 19, 20]. Later, a full phase diagram of CeBiSOF was mapped out, which shows SC and FM in a broad region of 0.4 1.0. Interestingly, both and achieve their maxima at 0.7 0.9, implying a joint origin for them. The magnetism in the Ce sublattice is revealed to be an Ising FM by neutron scattering. X-ray absorption measurements indicate that the fluorine doping decreases the Ce valence, and the Ce valence is essentially 3+ in the coexistence regime. It is also revealed that the Ce-valence variation accompanies with a systematic changes in the atomic local structures. Additionally, FM+SC has been found even in a Ce-diluted system SrCeFBiS. So far, the origin of FM+SC remains an open question.
EuBiSF is a newly discovered member in the BiS-based superconducting family, which exclusively shows a possible charge-density-wave (CDW) instability at 280 K and SC at 0.3 K without extrinsic doping. The uniqueness lies in the Eu mixed valence in connection with the crossing of Eu-4 bands onto the Fermi level. At 1.8 K the Eu-4 local moment possibly freezes into a spin-glass state. Since SC coexists with FM in Ce-diluted SrCeFBiS, it is of great interest to study the EuCeBiSF system to understand the interplay and compatibility between SC and the Ce/Eu-4 magnetism. In this paper, we report the physical properties of EuCeBiSF polycrystalline samples. We found that the Ce-4 moment orders ferromagnetically at 8 K, followed by a superconducting transition at 2.2 K. Meanwhile, a possible antiferromagnetic ordering of Eu-4 spins appears at 2.1 K. Our results demonstrate that EuCeBiSF is a rare example in which SC simultaneously coexists with complex 4 magnetism in a single material.
2 Experimental details
Polycrystalline samples of EuCeBiSF were synthesized by solid-state reactions under vacuum using powders of EuF (Alfa Aesar, 99.9%), BiS (99.995%) and S (99.9995%), and small pieces of Ce (99.8%). The stoichiometric mixtures were loaded in an alumina tube jacketed with an evacuated quartz ampoule which was then heated to 1000 K holding for 10 h. After cooling down, the mixtures were ground in an agate mortar, and pressed into pellets under a pressure of 2000 kg/cm. The pellets were sintered at 1000 K for 10 h in vacuum again. Note that all the procedures except for sample-heating and ampoule-sealing were conducted in a glove box filled with pure argon.
Powder x-ray diffraction (XRD) was performed at room temperature using a PANalytical x-ray diffractometer (Model EMPYREAN) with a monochromatic CuK radiation. The lattice parameters were obtained by least-squares fit with the correction of zero shift. Temperature-dependent resistivity was measured in a Cryogenic Mini-CFM measurement system by a standard four-terminal method. Gold wires were attached onto the samples’ surface with silver paint. The size of the contact pads leads to a total uncertainty in the absolute values of resistivity of 15%. Additional resistivity measurements down to 0.3 K were carried out in a He refrigerator inserted in a Oxford superconducting magnet system. Temperature-dependent of dc magnetization was performed on a Quantum Design Magnetic Property Measurement System (MPMS-5). The specific heat capacity was measured down to 0.5 K using a relaxation technique, on a Quantum Design Physical Property Measurement System (PPMS-9).
3 Results and discussion
Figure 1 shows the powder XRD data of the as-prepared EuCeBiSF sample. The XRD pattern can be indexed by a tetragonal lattice with the space group P4/nmm (No. 129). The unindexed reflections marked by asterisks are quite weak, which are identified to BiS impurity. We note that the Bragg-peak positions for a cubic CeS phase coincide with those of the main phase, and a multi-phase Rietveld refinement gives the amount of CeS of 3.3 at.%. The unreacted impurity would lead to a slightly reduced Ce concentration of 0.48, compared with the nominal one. Note that both BiS and CeS impurities will not significantely influence the physical properties below because of their low fractions. The fitted lattice parameter, = 4.0697(1) Å, is 0.47% larger than that of its parent compound EuBiSF. However, another lattice parameter, = 13.3286(6) Å, is 1.52% smaller. As a result, the value has a significant decrease. The remarkable change in the lattice parameters indicates the incorporation of Ce, which induces electrons into the BiS layers. Similar effect has been reported in many other BiS-based systems such as LaBiSO, CeBiSO, NdBiSO, and SrBiSF.
Shown in figure 2(a) is the temperature dependence of resistivity, , for the EuCeBiSF polycrystals. In contrast to EuBiSF, which exhibits metallic conduction and a CDW-like transition at 280 K, EuCeBiSF shows semiconducting-like behaviour with decreasing temperature before SC sets in. Note that is enhanced by 7 times (from 0.3 K to 2.2 K), accompanied by disappearance of the CDW-like transition. The enhancement can be understood by the additional electron doping with the Ce-for-Eu substitution. A very recent report shows the same enhancement in La-doped EuBiSF. Note that the semiconducting behaviour resembles those observed in other BiS-based materials[18, 30, 33], which is explained in terms of Anderson localization.
The resistive superconducting transitions under magnetic fields are shown in figure 2(b) and (c). With increasing external magnetic fields, decreases obviously and, the transitions become broader. Because of the broadened transitions as well as the semiconducting-like temperature dependence above , we define the onset transition temperature, , by the crossing point of the extrapolation straight lines from the two sides (the normal and superconducting states). Consequently, the upper critical fields were obtained, as shown in the figure 2(d). By using the Werthamer-Helfand-Hohenberg theory which applies to the orbital limited case, and the zero-temperature can be estimated to be 0.75 T, comparable to those in the FM-coexisted SrCeBiSF as well as nonmagnetic SrLaBiSF. The value is obviously lower than the Pauli paramagnetic limit = 1.84 4 T. Since the Ce-4 moment becomes ferromagnetically ordered at 8 K (see below), the unaffected upper critical field implies negligible coupling between the Cooper pairs and the Eu/Ce local moment.
There is a hump in just above for T. This anomaly is gradually suppressed to lower temperatures, and then is smeared out with increasing magnetic fields. The hump is possibly due to an antiferromagnetic ordering of Eu spins (more evidences will be given by the magnetic and specific-heat measurements below). We also note that the resistivity decreases with increasing magnetic field below 10 K. The negative magnetoresistance in the normal state was also observed in other SC and FM coexisted BiS-based superconductors. Similar negative magnetoresistance was earlier reported in EuFeAsP and CeFeAsPOF. The negative magnetoresistance comes from the ferromagnetic ordering for the Ce-4 moment (see below).
Figure 3(a) shows the dc magnetic susceptibility () measured under 1 kOe for EuCeBiSF. Considering the paramagnetic contributions from the local moments of both Eu and Ce ions, we fit the susceptibility by the formula, = + + , where the is the temperature independent term, and are the Curie-Weiss constants of Eu and Ce ions, respectively, and and are their corresponding paramagnetic Curie-Weiss temperatures. The data fitting in a broad temperature range of 10 K 400 K without any parameter controlling gives the effective moments of (Eu) = 8.7 /Eu and (Ce) = 2.34 /Ce, which basically agrees with the expected values (7.94 /Eu and 2.54 /Ce) for Eu and Ce ions. This result indicates that the Eu valence is essentially divalent, in contrast with the mixed valence in EuBiSF. In addition, the fitted and values (3.7 and 6.5, respectively) are consistent with the effective antiferromagnetic interactions between Eu ions and ferromagnetic interactions between Ce ions.
Below 10 K, increases rapidly with decreasing temperature, and it tends to saturate at lower temperatures, suggestive of a ferromagnetic transition. Another evidence of ferromagnetism is given by the divergence between zero-field-cooling (ZFC) and field-cooling (FC) susceptibility below 8 K, as shown in figure 3(b). Indeed, the field dependence of magnetization, shown in figure 4, displays a ferromagnetic-like hysteresis loop at 2 K, while such a hysteresis disappears at 10 K. The saturation magnetization is linearly extrapolated to be 0.27 /f.u. (’f.u.’ denotes formula unit), corresponding to a 0.54 /Ce. This ordered magnetization is significantly lower than the expected value of 1.0 /Ce. There are several possible reasons. First of all, the could be underestimated due to (1) magnetocrystalline anisotropy, (2) the existence of SC, and (3) the Eu magnetism. The second reason comes from the possible deviation of Ce concentration. As mentioned above, the real Ce concentration could be 0.48 concerning the formation of CeS impurity. The last possibility is that the Ce moment actually forms ferromagnetic clusters under low external fields.
The magnetization continues to increase with increasing magnetic field, and it tends to saturate at 4.4 /f.u., owing to a field-induced Eu-spin reorientation. The final saturation magnetization is approximately equal to the sum of half an Eu spin (3.5 ) and half a Ce moment (0.5 ). Compared with the reduced magnetization of 5.58 /Eu in EuBiSF due to the Eu mixed valence, the result further indicates that the Eu ions are divalent in EuCeBiSF.
The superconducting transition observed in the above resistivity measurement is not obvious for the magnetic data primarily because of the FM for Ce-4 moment. There is no Meissner effect, and even the magnetic shielding effect is not certain, similar to the previous reports[18, 19, 20]. Here, as shown in figure 3, a kink in the ZFC curve can be seen at 2.2 K, which could be due to the superconducting transition.
Figure 5 shows the temperature dependence of the specific heat, , for EuCeBiSF. The curve tends to saturate to 130 J mol K, basically consistent with the Dulong-Petit value 5 3 124.7 J mol K, the high-T limit for the lattice specific heat. The upper left inset magnifies the low- data. Two anomalies can be identified. The broad peak below 8 K is attributed to the ferromagnetic ordering of the Ce-4 moment. The second peak centered at 1.5 K is probably associated with the magnetic ordering for the Eu spins. A similar peak was observed in EuBiSF, which was interpreted as a spin-glass transition because the peak is relatively broad and the magnetic entropy of the transition is reduced. However, the peak here is remarkably narrower, and the magnetic entropy essentially corresponds to the magnetic LRO scenario. The negative value as well as the feature of curve at 2 K suggests antiferromagnetic order for the Eu spins. The superconducting specific-heat jump is hardly seen because of the reduced signal by the Ce-FM as well as the strong magnetic ’background’ due to Eu-AFM.
The specific heat is generally contributed from several origins including crystalline lattice or phonons (), conduction electrons (), and magnons (). The magnon contribution is expected to be negligible above 10 K, since no magnetic ordering takes place there. Then, we fit the data in the temperature range of 10 K 18 K by employing the Debye law, + . The Sommerfeld coefficient is fitted to be 127.0 mJ mol K, 1.7 times of that of EuBiSF (73.3 mJ mol K), 2.2 times of that of SrCeFBiS (58.6 mJ mol K), and 90 times of that of SrLaFBiS (1.42 mJ mol K). The great enhancement in Sommerfeld coefficient suggests the contributions owing to the Ce/Eu-4 electrons. The fitting also yields = 1.02 mJ mol K, from which the Debye temperature can be derived by the formula [(12/5)/]. The obtained Debye temperature (212.0 K) is reasonably higher than that of EuBiSF (201 K) and in between with those of LaBiSOF and YbBiSOF.
The temperature dependence of the released magnetic entropy (from zero temperature) can be obtained by the integration , where (here we approximately assume for 0 K 0.5 K). As shown in the lower inset of figure 5, the released entropy is just equal to 50% of ( for Eu) at 2.3 K where the Eu-4 spins become disordered. This strongly suggests that the Eu moment is fully ordered rather than partially ordered like that in a spin glass. When integrating to above the ferromagnetic transition temperature, additional 50% of ( for Ce) is released. This means that the Ce moment is also fully ordered at zero temperature. In short, our result indicates two types of magnetic LRO for the 4 moments, FM for the Ce moment and possible AFM for the Eu spins, both coexisting with SC in EuCeBiSF.
SC and FM are two antagonistic cooperative phenomena, and only in few special cases they can be compatible in a single material. So far, the uniform coexistence is believed to have realized exclusively in the uranium-based materials[37, 38, 39], in which both SC and FM come from the same type of electrons. The FM+SC in the EuFeAs-related systems[7, 8, 9, 10, 11] belongs to the case that SC and FM are from distinct electrons of different atoms, i. e. the Fe-3 and Eu-4 electrons. To be specific, SC is associated with the and orbitals of Fe 3 electrons while FM arises from the LRO of Eu-4 spins via the RKKY interactions mediated mainly through the and .
The EuCeBiSF bears similarities with the doped EuFeAs system, in which SC and FM emerge in different layers. Upon Ce doping, more electrons are doped into the BiS layers, which leads to the enhancement of SC. The Bi 6 orbitals mainly contribute to the electronic states near the Fermi level[40, 41, 42]. Furthermore, the 6 and 6 electrons are believed to be responsible for SC. It is expected that these superconducting electrons hardly couple with the 4 electrons since the Bi 6 and 6 orbitals do not overlap with the 4 orbitals located well above the BiS layers. This explains why SC is not influenced by the Ce/Eu-4 local moments.
For the complex local-moment LRO, we note that the evolution of the magnetic ordering for the Ce-4 moment and the Eu-4 spin is very different. The Ce-FM is induced, accompanied with the emergence of SC, by the electron doping[22, 26]. Therefore, the Ce-FM is probably due to a RKKY exchange interaction in which the Bi-6 electrons might play an important role. This scenario actually resembles the case in doped EuFeAs, which simultaneously enables SC for 6 and 6 electrons in the BiS layer and FM for the Ce-4 moment mediated mainly by the 6 itinerant electrons. For the Eu-AFM, on the other hand, the magnetic transition temperature, which is explicitly shown by the specific-heat peak, is essentially the same as that of the undoped EuBiSF. This suggests that the Eu-AFM is not primarily due to a RKKY interaction. Considering the random occupation in the crystallographic site, such a magnetic LRO is not likely to happen through a superexchange interaction, either. Here we argue that the magnetic dipolar interaction could be the origin for the Eu-AFM. The nearest-neighbor dipolar coupling will be always antiferromagnetic for spins parallel to the axis, although Eu ions are randomly occupied in the lattice. Additionally, the high spins of Eu ions makes the magnetic interaction strong enough to form a magnetic order at about 2 K.
There are still some open questions. What is the magnetic interaction between Eu spins and Ce moment? What are the Eu/Ce spin directions in the lattice? Why Eu spins do not become ferromagnetic via a RKKY interaction, like the Ce moment?
5 Concluding remarks
In summary, we demonstrate that EuCeBiSF is an interesting material which shows coexistence of superconductivity, ferromagnetism and possible antiferromagnetism. Superconductivity emerges in the BiS layers, while the long-range magnetic ordering arises from the (Eu,Ce)F layers. Strikingly, the superconducting transition temperature as well as the upper critical field is hardly suppressed by the ferromagnetism for the Ce-4 moment. By analogy with the scenario in EuFeAs-related ferromagnetic superconductors[3, 8], we tentatively interpret it by considering different Bi-6 orbitals that are responsible for superconductivity itself and for mediating the RKKY interaction, respectively. The antiferromagnetism of the Eu-4 spins is possibly due to a magnetic-dipole interaction. Further experimental and theoretical works are called for to confirm the interesting phenomenon and to clarify the underlying physics.
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