Correlation effects of exchange splitting and coexistence of spin-density-wave and superconductivity in single crystalline Sr{}_{1-x}K{}_{x}Fe{}_{2}As{}_{2}

Correlation effects of exchange splitting and coexistence of spin-density-wave and superconductivity in single crystalline SrKFeAs

Y. Zhang, J. Wei, H. W. Ou, J. F. Zhao, B. Zhou, F. Chen, M. Xu, C. He, G. Wu, H. Chen, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, X. H. Chen, D. L. Feng dlfeng@fudan.edu.cn Department of Physics, Surface Physics Laboratory (National Key Laboratory), and Advanced Materials Laboratory, Fudan University, Shanghai 200433, P. R. China Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China Hiroshima Synchrotron Radiation Center and Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.
July 15, 2019
Abstract

The nature of spin-density wave and its relation with superconductivity are crucial issues in the newly discovered Fe-based high temperature superconductors. Particularly it is unclear whether the superconducting phase and spin density wave (SDW) are truly exclusive from each other as suggested by certain experiments. With angle resolved photoemission spectroscopy, we here report exchange splittings of the band structures in SrKFeAs (), and the non-rigid-band behaviors of the splitting. Our data on single crystalline superconducting samples unambiguously prove that SDW and superconductivity could coexist in iron-pnictides.

pacs:
74.25.Jb,74.70.-b,79.60.-i,71.20.-b

Both the cuprates and the iron pnictides high temperature superconductors are in the vicinity of certain magnetic order PCDai (). For the cuprate, the antiferromagnetic spin fluctuations might likely facilitate the -wave pairing, which makes the nature of the spin density wave (SDW) in the iron pnictides and its relation with the superconductivity central issues. Recently, we found that exchange splittings of the bands (instead of Fermi surface nesting) are responsible for the SDW formation in BaFeAsYangExchange (). This is beyond the prediction of all the existing band structure calculations. Particularly, the momentum and band dependence of the splitting, and the anomalously small Stoner ratio (the ratio of exchange splitting over magnetic moment) illustrate the unusual properties of the SDW order. The detailed behaviors of the exchange splitting thus need to be uncovered to further understand its microscopic origin.

One relevant question is whether SDW and superconductivity can coexist at certain region of the phase diagram. Early resistivity data have indirectly suggested that SDW and superconductivity could coexist in LaOFFeAsJACS (), SmOFFeAsLiu (). However, more recent neutron diffraction, muon spin relaxation (SR), and Mössbauer spectroscopy indicate that they are exclusive from each other for CeOFFeAs ZhaoNeutron () and LaOFFeAs LuetkensNuclear (). The anomaly in resistivity is associated with the structural transition rather than the SDW. On the other hand, the situation seems to be quite different for BaKFeAs, it has been shown recently that the SDW and superconductivity could coexist in polycrystalline samples for based on combined transport, x-ray and neutron diffraction studiesChenBao (). If one could rule out the caveat of possible phase segregation, this would allude to a new ground state in BaKFeAs, where Cooper pairs are formed on a SDW background. This resembles the Hg-based five-layer cuprate, where antiferromagnetic order coexists with the superconductivity uniformly within single plane NMR (). Novel properties might be expected.

Figure 1: Relative resistance (with respect to the resistance at 280K) of SrKFeAs () vs. temperature. The and curves are shifted up by 0.25 and 1 respectively.
Figure 2: (color online) Electronic structure of SrFeAs. (a) Photoemission intensity along the cut as indicated in panel d. (b) The second derivative of the data in panel a. (c) The MDC’s near Fermi energy for the data in panel a. (d) Photoemission intensity map at in the Brillouin zone, where the measured Fermi surface sheets are shown by dashed curves. Only one set of Fermi surface around M is shown for a clearer view. Data were taken at 230K. (e,f,g,h) are the same as in panel a,b,c,d respectively, but taken at 10K.
Figure 3: (color online) Electronic structure of SrKFeAs. (a) Photoemission intensity along the cut as indicated in panel d. (b) The second derivative of the data in panel a. (c) The MDC’s near for the data in panel a. (d) Photoemission intensity map at in the Brillouin zone. Data were taken at 150K. (e,f,g,h) are the same as in panel a,b,c,d respectively, but taken at 10K.

In this Letter, we report angle resolved photoemission spectroscopy (ARPES) measurements of SrKFeAs single crystals. SrFeAs has the highest known SDW transition temperature () of about 205K in iron pnictides Sr (). We show that the exchange splitting occurs in SrKFeAs for the doping concentration with onset temperatures and amplitudes in descending order. The systematics shows that the exchange splitting is a fingerprint of the SDW on the electronic structure. Therefore, our results on single crystalline samples prove that superconductivity and SDW could coexist in SrKFeAs (superconducting transition temperature ). The phase diagram of the SrKFeAs thus would be very different from that of the iron oxypnictide. Moreover, the quite different manifestations of the exchange splitting in various systems further highlight its complexity and correlated nature, providing a new set of clues for sorting out the microscopic mechanism of the splitting.

The SrKFeAs () single crystals were synthesized with tin flux method singleSr (), where the doping is determined through energy-dispersive x-ray (EDX) analysis. The resistivity data in Fig. 1 indicate that the undoped compound () enters the SDW state at about , and there is an anomaly at 168K for , while the compound enters the zero resistance superconducting phase at about 25K. ARPES measurements were performed with 24 eV photons from beamline 5-4 of Stanford synchrotron radiation laboratory (SSRL) and beamline 9 of Hiroshima synchrotron radiation center. With Scienta R4000 electron analyzers, the overall energy resolution is 10meV, and angular resolution is 0.3 degree. The samples were cleaved in situ, and measured under ultra-high-vacuum of torr.

Figure 4: (color online) Temperature dependence of the band dispersion along the cut for SrKFeAs. Second derivative of photoemission intensity with respect to energy (a-f) for at 230K, 200K, 195K, 190K, 100K, and 10K respectively, (h-l) for at 170K, 160K, 150K, 40K, and 10K respectively, and (n-s) for at 150K, 145K, 140K, 130K, 100K, and 10K respectively. Dashed lines are the guides of eye for the bands. Note the minimum of the second derivative represents a peak, thus the lower part (red or white color) represents the band. (g), (m) and (t) are the temperature evolution of EDC’s at for and respectively. Note the momentum window is slightly wider for data.

The normal state band structure of SrFeAs is presented through the photoemission intensity and its second derivative with respective to energy along the cut [Figs. 2(a) and 2(b)]. Three bands (named as , and band respectively) could be identified to cross , with the assistance from the momentum distribution curves (MDC’s) in Fig. 2(c). Near M, the and bands become quite flat and degenerate within the experimental resolution, and do not cross the Fermi energy. There are thus two hole-type Fermi surfaces around , and one electron-type Fermi surface around M [Fig. 2(d)], as predicted by the band structure calculations LDA0 (); LDA1 (); LDA2 (); LDA3 (); LDA4 (); LDA5 (); NLWang2 (). In the SDW state, the data along the same cut are measured for comparison [Figs. 2(e-g)]. Three Fermi crossings (’s) could be clearly resolved near . The separation between the two ’s on both sides of is closer, giving a smaller hole pocket than the normal state one. The band is pushed away from , and splits into two bands, which are assigned as and respectively. Around M, the normal-state flat feature splits into three bands and well connected to features around . Correspondingly, the band is pushed down by about 60 meV; the band is pushed up to cross the Fermi energy; and the band is more or less unaffected. Moreover, the electron-like nature of the pocket could be better resolved in Figs. 2(f-g) than in the normal state, and its does not show any noticeable movement. Since Fermi surface folding in the SDW state is not observed, the SDW state has two more hole pockets, one around and one around M [Fig. 2(h)] than the normal state. Similar to the BaFeAs case, no energy gap is observed for all the bands at their ’s, ruling out the “Fermi-surface-nesting” mechanism for SDW in itinerant electron systems like Chromium and its alloys chromium ().

The corresponding electronic structure in the hole-doped SrKFeAs superconductor is illustrated in Fig. 3. At high temperatures [Fig. 3(a-d)], it is similar to that in the normal state of SrFeAs. As expected, the two hole pockets around grow larger, and the electron pocket around M slightly shrinks with hole doping. At 10K, there is no obvious splitting near . The most prominent difference occurs midway in the -M cut, where two features are observed in Figs. 3(f) and 3(g), one of which (the band) crosses , and gives an additional large hole pocket around M at 10K in Fig. 3(h).

To further illustrate the nature of splitting, detailed temperature dependence of the bands in SrKFeAs () are shown through the second derivative of the photoemission intensity in Fig. 4. For SrFeAs, although no obvious temperature dependence is observed for the band within the experimental resolution, the splitting of the band occurs abruptly between 200K and 195K Figs. 4(b-c), and develops rapidly with the decreasing temperatures. At the lowest temperature, the hybridization of the and could also be resolved clearly when they cross. However, the bands are named as if they were not crossing.

For and , band splittings occur very abruptly as well. The onset temperatures are estimated to be and for and respectively, as shown in Figs. 4(h-l) and Figs. 4(n-s). The splitting is momentum dependent in all cases. By extracting the largest splitting between the and bands at the of (which are close to their splittings at M by fit), one gets 120 meV, 85 meV, and 60 meV respectively for , and respectively, consistent with the decreasing onset temperatures of the splitting. As a comparison, the splitting around is just about 50 meV for . We note for BaFeAs, , and the maximal splitting is about 75  meV near M YangExchange (); both are close to the SrKFeAs case. Furthermore, all systems show similar spectral characters when the splitting are the most obvious. For example, the temperature evolutions of photoemission spectra at are quite similar in Figs. 4(g), 4(m) and 4(t) for respectively.

The band splitting occurs almost exactly at their bulk SDW transition temperatures for both SrFeAs and BaFeAs, and at the resistivity anomaly temperature of SrKFeAs. Considering that drops rapidly with doping ChenBao (), plus the drastically different low temperature band structures, one can conclude that the measured electronic structure reflects the bulk properties, and rule out any phase separation effects in all data. Similar to BaFeAs YangExchange (), such a splitting on the order of several and its temperature dependence cannot be explained by factors such as structure transition or spin orbital coupling. Instead, it can be most naturally explained by the exchange splitting associated with the SDW formation. In fact, the electronic energy of the system can be saved through such a splitting, and thus it can be responsible for the SDW. Consistently, the band splitting is of the same scale as the exchange interactions between the nearest and next-nearest neighbor local moments estimated from LDA calculationsYangExchange (); Lu (). In this regard, the observed systematics, such as the correlations among doping/onset temperature/splitting amplitude, and similar spectral characters indicate that the origin of band splittings in SrKFeAs is no different from others. Therefore, our results on single crystalline samples provide a compelling piece of evidence for the coexistence of the SDW and superconductivity in an iron pnictide.

The paramagnetic state electronic structures of various iron pnictides qualitatively resemble each other YangExchange (); DHLu (); XJZhouSC (); DHSC (); Kami (), regardless of the chemical environment or doping, as exemplified here for SrKFeAs. Nevertheless, Fig.4 also illustrates that the detailed behaviors of exchange splitting in various system can be rather different besides their similarities mentioned above. Take the splitting at M as an example, the shifts of both the and bands are equally strong from the normal state position, and the band does not split for ; for , shifts much more than , and its band shows a shift; for , only shows obvious shift. While for BaFeAs, all bands shift strongly at MYangExchange (). Particularly, the electron Fermi pocket around M splits into one large and one small electron pockets in BaFeAs; but for SrFeAs, the size of the pocket does not change noticeably, indicating a negligible splitting. Similarly, one could find further differences for exchange splitting around as well. These nontrivial findings unveil the correlated/non-rigid-band aspect of the exchange splitting.

The coexistence of SDW and superconductivity has profound consequences on the nature of the superconductivity. It not only suggests that the superconducting gap might open at one more () Fermi surface sheet in this material than in the BaKFeAs reported earlier XJZhouSC (); DHSC (). Because a split band is either majority or minority band that is in-phase or out-of-phase with the SDW spin order respectively, take a Cooper pair based on electrons at of a majority band in the singlet pairing channel for example, its spin-up electron and spin-down electron must be mainly situated in the spin-up and spin-down sites of the SDW respectively. This gives a novel ground state that is not known before. Moreover, because the SDW does not open an gap at , how it competes with the superconductivity in iron pnictides would be another interesting issue. On the other hand, the magnetic fluctuations related to SDW might even play a constructive role in superconductivity as in cuprates. We leave the detailed studies of these issues to future.

To summarize, we have measured the electronic structures of SrKFeAs. We show that besides the quantitative differences, the detailed behaviors of the splitting differ prominently in various iron pnictides. Since band structure calculations so far failed to reproduce or predict the observed exchange splitting, our results provide important new clues for revealing the microscopic origin of the exchange splitting and SDW in iron pnictides. Particularly, we show in the single crystalline SrKFeAs that SDW and superconductivity could coexist, revealing a new kind of ground state, which would help understand the relationship between the SDW and superconductivity in iron pnictides.

We thank Dr. W. Bao for inspiring discussions, and Dr. D. H. Lu and Dr. R. G. Moore for their experimental assistance at SSRL. This work was supported by the Nature Science Foundation of China, the Ministry of Science and Technology of China (National Basic Research Program No.2006CB921300), and STCSM. SSRL is operated by the DOE Office of Basic Energy Science under Contract No. DE-AC03-765F00515.

Note added in support: During preparation of this manuscript, a similar finding on SDW/superconductivity coexistence in (Ba,K)FeAs, (Sr,Na)FeAs, and CaFeAs is posted online based on SR experimentsmuSR ().

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