Low-energy spin excitations in Li(0.8)Fe(0.2)ODFeSe superconductor studied with inelastic neutron scattering
Mingwei Ma, Lichen Wang, Philippe Bourges, Yvan Sidis, Sergey Danilkin, Yuan Li
LLow-energy spin excitations in (Li . Fe . )ODFeSe superconductor studied withinelastic neutron scattering Mingwei Ma, ∗ Lichen Wang, ∗ Philippe Bourges, Yvan Sidis, Sergey Danilkin, and Yuan Li
1, 4, † International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China Laboratoire L´eon Brillouin, CEA-CNRS, Universit´e Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France Bragg Institute, Australian Nuclear Science and Technology Organization,New Illawarra Road, Lucas Heights NSW-2234, Australia Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
We report an inelastic neutron scattering study of single crystals of (Li . Fe . )ODFeSe.Temperature-dependent low-energy spin excitations are observed near Q = (0.5, 0.27, 0.5) andequivalent wave vectors symmetrically surrounding Q = (0.5, 0.5, 0.5) in the 1-Fe Brillouin zone,consistent with a Fermi-surface-nesting description. The excitations are broadly distributed in en-ergy, ranging from 16 to 35 meV. Upon cooling below the superconducting critical temperature ( T c ),magnetic response below twice the superconducting gap 2∆ SC exhibits an abrupt enhancement, con-sistent with the notion of spin resonance, whereas the response at higher energies increases moregradually with only a weak anomaly at T c . Our results suggest that (Li . Fe . )ODFeSe might beon the verge of a crossover between different Cooper-pairing channels with distinct symmetries. PACS numbers: 74.70.Xa, 78.70.Nx, 74.20.Rp, 74.25.Ha
A pivotal issue concerning the Cooper-pairing mech-anism in the Fe-based superconductors (FeSCs) is thepairing symmetry, which is commonly regarded as an im-portant thread for distinguishing among different theo-retical proposals. Pairing mediated by electron-phononinteractions [1] and/or orbital fluctuations [2] is expectedto occur in the plain s -wave ( s ++ ) channel, whereas pair-ing mediated by spin fluctuations [3] is expected to havesign-reversal behaviors in the gap function and occur inthe extended s -wave ( s + − ) or the d -wave channel [4–7].When hole pockets are present at the Γ point, it has beenreasonably well established that the predominant pairingsymmetry is s + − [8, 9], which favors the unconventionalpairing mechanism associated with spin fluctuations. Butbecause the FeSCs are multi-orbital systems with multi-ple magnetic exchange interactions that are comparablein strength [10], the preference on one pairing channelover another may further depend on the Fermi-surface(FS) topology [5, 11]. Therefore, the assumption that auniversal pairing mechanism applies to all FeSCs requiresa more stringent test, namely, pairing symmetry needsto be determined and compared with theory for systemswith very different band filling and FS topologies.An important case of distinct FS topology was firstestablished in alkali-metal intercalated Fe selenides [12],which have no hole pocket at the Γ point as a resultof heavy electron doping [13–15]. Later it became clearthat the electron doping can be achieved with variousmethods, including intercalation into bulk FeSe [16–21],epitaxial growth of a single atomic layer of FeSe on acharge-transferring SrTiO substrate (FeSe/STO) [22–24], and surface dosing of FeSe with potassium [25–27],all of which end up with similar electronic structures. It isintriguing that the absence of hole pockets at the Γ pointis empirically linked to the much higher values of T c than in bulk FeSe [28]. The associated pairing symmetry isconsidered to be of great theoretical importance but hasremained unsettled [11, 29–35], in part because of seem-ingly contradictory results from inelastic neutron scat-tering (INS) and scanning tunneling spectroscopy (STS)experiments: On the one hand, the observation of a spinresonance below T c in INS studies of A x Fe − y Se ( A =Rb, Cs, K) [36–38] points towards a gap function with op-posite signs on the electron pockets [30, 33]. On the otherhand, the inability of non-magnetic impurities to createin-gap states in FeSe/STO suggests that the pairing sym-metry is plain s -wave [39]. Notably, both of these systemshave material-specific aspects that are not representativeof all FeSCs. The superconductivity in A x Fe − y Se oftensuffers from a low volume fraction [40], probably due tothe requirement of a high density of Se vacancies and/orof a particular type of interfaces [41], whereas the super-conductivity in FeSe/STO may be strongly assisted byphonons in the substrate [42, 43].In order to assess the universality of the previous re-sults and address the contradictions, it is desirable toinvestigate a phase-pure bulk material without a sub-strate. The newly discovered (Li . Fe . )OHFeSe super-conductor offers such an opportunity [18, 19], since itdoes not show substantial chemical phase separation andis stable in air. Photoemission experiments have demon-strated that (Li . Fe . )OHFeSe has a FS topology rep-resentative of that of heavily-electron-doped FeSe sheets[20, 21]. Here we report our INS study of fully-deuterated(Li . Fe . )ODFeSe single crystals, aiming to character-ize the low-energy spin fluctuations. We find that thetemperature-dependent magnetic signals are centered atmomentum positions consistent with a FS-nesting pic-ture, but the signal is rather widely distributed in energyand extends well above twice the superconducting en- a r X i v : . [ c ond - m a t . s up r- c on ] N ov FIG. 1. Temperature dependence of magnetic susceptibilityof (Li . Fe . )ODFeSe measured with a magnetic field of 10Oe applied perpendicular to the c axis after zero-field cool-ing. Left inset: photo of our co-aligned sample for INS ex-periments. Right inset: x -ray Laue-reflection pattern from asingle crystal ( x -rays incident along the c axis). ergy gap 2∆ SC . While the enhancement of signals below2∆ SC has a temperature dependence consistent with thatof a spin resonance in unconventional superconductors,the signal above 2∆ SC exhibits a more gradual increasebelow T c . The fact that these two parts of signals arecomparable in strength despite their distinct tempera-ture dependence suggests that (Li . Fe . )OHFeSe, andperhaps heavily-electron-doped FeSe sheets in general,might host two types of pairing interactions that are fa-vorable for distinct pairing symmetries.Our triple-axis INS experiments were performed onthe spectrometer 2T at the Laboratoire L´eon Bril-louin (LLB), France and on the spectrometer TAIPANat the Bragg Institute of Australian Nuclear Scienceand Technology Organization. The sample consistedof over one hundred single crystals of fully-deuterated(Li . Fe . )ODFeSe, which were grown with a hydrother-mal reaction method [44] and coaligned in the ( H , K , H ) scattering plane. Here and throughout the paper,reciprocal-space vectors are quoted in reciprocal-latticeunits (r.l.u.) under the notation of the 1-Fe Brillouinzone, with unit-cell parameters a = b = 2 . c = 9 . x -ray Laue reflections and a sharpincrease of diamagnetic signals below T c = 39 K demon-strate the high quality of our sample (Fig. 1). The INSdata were collected in fixed- k f mode ( k f = 3 . − ) us-ing a focusing pyrolytic graphite (PG) monochromatorand analyzer. Additional PG filters were placed betweenthe sample and the analyzer to eliminate higher-ordercontaminations.Figure 2(a) displays the result of momentum ( Q ) scansat a fixed energy of 18 meV, performed along the trajec-tory (0.5, K , 0.5) and at temperatures both below andabove T c . As an effort to search for the spin resonance, FIG. 2. (a) Q scans along the (0.5, K , 0.5) direction ata fixed energy transfer of 18 meV and temperatures of 4 Kand 42 K. (b) Intensity difference between the two temper-atures. (c) Q scans at 21 meV in a direction perpendicularto that in (a). (d) The intensity difference between the twotemperatures in (c). Arrows indicate the fitted peak centers. this trajectory was chosen after the previously reportedresults for Rb x Fe − y Se [36], since the two materials havesimilar electronic structures. The energy was chosen tobe about 64% [45] of the maximal superconducting gap2∆ SC , which has been previously determined to be about28.6 meV [46]. Despite the use of a fully-deuterated sam-ple, the background scattering is very strong due to thesizable neutron incoherent scattering cross sections of theD ( H) and Li isotopes. Therefore, we use the intensitydifference between the two temperatures to extract themagnetic signals [Fig. 2(b)], and find a net intensity in-crease below T c near Q ± = (0 . , . ± . , . Q ± positions are symmetricaround (0.5, 0.5, 0.5), they are physically equivalent. Thedata suggest that the signal amplitude is slightly largerat Q − , consistent with the expectation that the form fac-tor decreases with increasing | Q | for magnetic scattering.The data also show that there is no intensity enhance-ment below T c at (0.5, 1.0, 0.5) which is equivalent to(0.5, 0, 0.5), where the strongest increase of magnetic sig-nals below T c is commonly observed in FeSCs with holepockets at the Γ point [9]. We emphasize that the totalmagnetic signals at Q ± may be substantially greater thanthe peak amplitudes displayed in Fig. 2(b), which onlycorrespond to the part of signals that changes below T c .The total magnetic signal is difficult to estimate from ourdata due to the presence of strongly Q -dependent phononscattering at nearby energies [Fig. 3(a)], which explainsthe strong variation of intensity versus Q in Fig. 2(a).In order to pin down the Q position that has thestrongest ( T -dependent) magnetic signal, we have per-formed Q scans along the perpendicular direction ( H , FIG. 3. (a) Energy scans at fixed Q positions (0.5, 0.68, 0.5)and (0.5, 0.73, 0.5) in the superconducting state ( T = 4 K)and normal state ( T = 42 K). (b) Intensity difference betweenthe two temperatures. H ) going through Q − , and the data [Fig. 2(c-d)]confirm that the magnetic signals are centered on thehigh-symmetry line (0.5, K , 0.5). Therefore, the distri-bution of magnetic signals in the Q space is overall verysimilar to that in A x Fe − y Se ( A = Rb, Cs, K) [36–38].A similar interpretation, that the characteristic Q ± fol-low from a FS-nesting picture with sign-reversal pairing[30, 33], also applies here.Figure 3 displays energy scans performed at Q = (0.5,0.68, 0.5) and (0.5, 0.73, 0.5) over an extensive energyrange, and again we use the intensity difference between4 K and 42 K to reveal the magnetic signals. We con-sider both of these Q positions to be sufficiently closeto Q + given the large momentum widths of the signalsin Fig. 2(b). Similar measurements cannot be performednear Q − due to neutron kinematic constraints in the scat-tering process. Surprisingly, it turns out that the energiesthat we have chosen (18 and 21 meV) for the measure-ments in Fig. 2 belong to a rather broad distribution ofintensity enhancement below T c , ranging from 16 meV toabout 35 meV. In fact, the globally greatest net intensityincrease occurs at about 30 meV. Below 16 meV, a strongdecrease of intensity is observed upon cooling from 42 Kto 4 K, due to both opening of the superconducting gapand reduction in thermally-activated phonon scattering.Motivated by the broad energy distribution, we haveperformed detailed measurements of the T dependence ofthe scattering signal, at both 21 meV and 31 meV. Theresults are displayed in Fig. 4. For 21 meV the measure-ment was performed at Q − , where the kinematic con-straints can still be satisfied and the signal is stronger,whereas for 31 meV the measurement could only be per-formed at Q + . The difference in Q explains the seem-ingly different relative intensities at these two energiescomparing Fig. 4 and Fig. 3(b). At 21 meV, the mag-netic signal exhibits an order-parameter-like increase be-low T c , and is therefore consistent with being a spin reso-nance [9, 45]. In contrast, the signal at 31 meV exhibits acontinuous increase towards the lowest temperature withonly a weak (if any) anomaly at T c . FIG. 4. (a) T dependence of INS signal at Q = (0.5, 0.27,0.5) and 21 meV. (b) T dependence of INS signal at Q = (0.5,0.73, 0.5) and 31 meV. Averaged intensities just above T c areset to zero. Solid lines are guide to the eye. Very recently and after the completion of our ex-periments, there were two reports of INS studies of(Li . Fe . )ODFeSe using powder [47] and single-crystal[48] samples. Here we compare our data to the pre-viously reported ones, as there are several quantita-tive differences at first glance: (1) The in-plane posi-tions of Q ± were estimated to be (0 . , . ± .
17) inRef. 47 and (0 . , . ± .
18) in Ref. 48, whereas we find(0 . , . ± . ≈
23 meV [47] and 21 meV[48], with relatively weak and nearly no T -dependent in-tensities above 28 meV ≈ SC , respectively, whereashere we still find a substantial increase of magnetic scat-tering below T c at 31 meV despite the distinct temper-ature dependence in Fig. 4. (3) The momentum widthof the resonance was previously found to be larger inthe transverse direction with respect to the displacementaway from (0.5, 0.5) [48]. In our data, the width ap-pears to be larger in the longitudinal direction (Fig. 2),although the statistical accuracy is still too limited forus to make a firm conclusion here.An important difference between our measurementsand the previous single-crystal study [48] is the out-of-plane momentum transfer, which was chosen here to be0.5 r.l.u. and zero in the previous triple-axis INS ex-periments. It is possible that the energy and in-planemomentum distribution of magnetic signals is sensitiveto the choice of the out-of-plane momentum transfer, be-cause of FS warping [49, 50] and/or variation of 2∆ SC with k z [51]. To our knowledge, no similar investigationshave been reported so far for (Li . Fe . )OHFeSe. In-deed, according to the time-of-flight INS data displayedin Figs. 2 and 3 of Ref. 48, which integrate over a widerange of out-of-plane momentum transfer, the low-energymagnetic signals are centered at in-plane Q positions veryclose to our result. Moreover, in the previous powderstudy [47] where magnetic signals integrated over a broadrange in | Q | were used to construct the energy distribu-tion, a noticeable amount of intensity increase below T c was present above 2∆ SC . We therefore conclude that theabove differences are primarily related to the out-of-planemomentum transfer, although additional variations re-lated to the samples, such as the precise electron doping,may also play a role.The overall phenomenon in Fig. 3 is somewhat similarto the “even-parity” spin resonance in heavily hole-dopedhigh- T c cuprates, in which case the feature becomes verybroad as its energy approaches 2∆ SC [52, 53], whereas the“odd-parity” counterpart at lower energy is considerablysharper. Although the presence of two resonant modeshas also been reported in the pnictides [54, 55], we believethat it is unrelated to our observation, since the signals at21 and 31 meV have different T dependence, and because31 meV is clearly above SC [20, 21, 46]. The fact thatthe response above 2∆ SC is smoothly connected to theresonance at 21 meV [47, 48] suggests that the supercon-ductivity in (Li . Fe . )OHFeSe might be supported bytwo types of pairing interactions. The first type, presum-ably related to spin fluctuations, is in favor of pairing ina sign-reversed fashion which leads to the formation of aspin resonance below 2∆ SC ; the second type, possibly re-lated to electron-phonon interactions and/or orbital fluc-tuations, is in favor of plain s -wave pairing, which simplyleads to a pile-up of magnetic spectral weights just above2∆ SC [56] in the superconducting state. The apparent de-pendence of the signals above 2∆ SC on the out-of-planemomentum transfer, as discussed above, suggests thatthe second type of pairing interactions might be furtherselective to the k z quantum number of the quasiparticles.Finally, our results are likely related to the re-cent observation of similar phenomena in sulfur-dopedK x Fe − y Se [57], which were interpreted as evidence fora transition from sign-reversed to sign-preserved Cooperpairing. The transition was observed upon a simulta-neous suppression of 2∆ SC and T c by sulfur doping,which does not seem to affect the characteristic ener-gies of the spin fluctuations. It is therefore plausible thatthe second type of pairing interactions in sulfur-dopedK x Fe − y Se are capable of supporting superconductiv-ity with T c up to ≈
25 K [57]. In comparison to that,(Li . Fe . )OHFeSe can be viewed as FeSe sheets inter-calated with molecules containing much lighter atoms.Hence, if the second type of pairing interactions are asso-ciated with phonons in structural units next to the FeSesheets, such as in the substrate of FeSe/STO [42, 43],the interactions will be able to support superconductiv-ity in (Li . Fe . )OHFeSe up to higher temperatures thanin K x Fe − y Se . This is consistent with our observationof magnetic signals above 2∆ SC already in a T c = 39K sample, as well as with the experimental evidence forpredominant plain s -wave pairing [39] in FeSe/STO witheven higher T c .We wish to thank Jitae Park and Fa Wang for dis-cussions. This work is supported by the National Natu-ral Science Foundation of China (Grants No. 11374024 and No. 11522429) and Ministry of Science and Tech-nology of China (Grants No. 2015CB921302 and No.2013CB921903). ∗ These authors contributed equally to this study. † [email protected][1] L. Boeri, O. V. Dolgov, and A. A. Golubov, Phys. Rev.Lett. , 026403 (2008).[2] H. Kontani and S. Onari, Phys. Rev. Lett. , 157001(2010).[3] D. J. Scalapino, Rev. Mod. Phys. , 1383 (2012).[4] I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du,Phys. Rev. Lett. , 057003 (2008).[5] K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka,H. Kontani, and H. Aoki, Phys. Rev. Lett. , 087004(2008).[6] K. Seo, B. A. Bernevig, and J. Hu, Phys. Rev. Lett. ,206404 (2008).[7] Q. Si and E. Abrahams, Phys. Rev. Lett. , 076401(2008).[8] T. Hanaguri, S. Niitaka, K. Kuroki, and H. Takagi, Sci-ence , 474 (2010).[9] P. Dai, Rev. Mod. Phys. , 855 (2015).[10] T. Yildirim, Phys. Rev. Lett. , 057010 (2008).[11] T. Saito, S. Onari, and H. Kontani, Phys. Rev. B ,140512 (2011).[12] J. Guo, S. Jin, G. Wang, S. Wang, K. Zhu, T. Zhou,M. He, and X. Chen, Phys. Rev. B , 180520 (2010).[13] D. Mou, S. Liu, X. Jia, J. He, Y. Peng, L. Zhao, L. Yu,G. Liu, S. He, X. Dong, J. Zhang, H. Wang, C. Dong,M. Fang, X. Wang, Q. Peng, Z. Wang, S. Zhang, F. Yang,Z. Xu, C. Chen, and X. J. Zhou, Phys. Rev. Lett. ,107001 (2011).[14] Y. Zhang, L. X. Yang, M. Xu, Z. R. Ye, F. Chen, C. He,C. H. Xu, J. Jiang, B. P. Xie, J. J. Ying, X. F. Wang,X. H. Chen, J. P. Hu, M. Matsunami, S. Kimura, andD. L. Feng, Nature Mater. , 273 (2011).[15] T. Qian, X.-P. Wang, W.-C. Jin, P. Zhang, P. Richard,G. Xu, X. Dai, Z. Fang, J.-G. Guo, X.-L. Chen, andH. Ding, Phys. Rev. Lett. , 187001 (2011).[16] T. P. Ying, X. L. Chen, G. Wang, S. F. Jin, T. T. Zhou,X. F. Lai, H. Zhang, and W. Y. Wang, Sci. Rep. , 426(2012).[17] J. Guo, H. Lei, F. Hayashi, and H. Hosono, Nature Com-mun. , 4756 (2014).[18] X. F. Lu, N. Z. Wang, H. Wu, Y. P. Wu, D. Zhao, X. Z.Zeng, X. G. Luo, T. Wu, W. Bao, G. H. Zhang, F. Q.Huang, Q. Z. Huang, and X. H. Chen, Nature Mater. , 325 (2015).[19] X. Dong, H. Zhou, H. Yang, J. Yuan, K. Jin, F. Zhou,D. Yuan, L. Wei, J. Li, X. Wang, G. Zhang, and Z. Zhao,JACS , 66 (2015).[20] L. Zhao, A. Liang, D. Yuan, Y. Hu, D. Liu, J. Huang,S. He, B. Shen, Y. Xu, X. Liu, L. Yu, G. Liu, H. Zhou,Y. Huang, X. Dong, F. Zhou, K. Liu, Z. Lu, Z. Zhao,C. Chen, Z. Xu, and X. Zhou, Nature Commun. , 10608(2016).[21] X. H. Niu, R. Peng, H. C. Xu, Y. J. Yan, J. Jiang, D. F.Xu, T. L. Yu, Q. Song, Z. C. Huang, Y. X. Wang, B. P.Xie, X. F. Lu, N. Z. Wang, X. H. Chen, Z. Sun, and D. L. Feng, Phys. Rev. B , 060504 (2015).[22] Q. Wang, Z. Li, W. Zhang, Z. Zhang, J. Zhang, W. Li,H. Ding, Y. Ou, P. Deng, K. Chang, J. Wen, C. Song,K. He, J. Jia, S. Ji, Y. Wang, L. Wang, X. Chen, X. Ma,and Q. Xue, Chin. Phys. Lett. , 037402 (2012).[23] S. He, J. He, W. Zhang, L. Zhao, D. Liu, X. Liu, D. Mou,Y. Ou, Q. Wang, Z. Li, L. Wang, Y. Peng, Y. Liu,C. Chen, L. Yu, G. Liu, X. Dong, J. Zhang, C. Cheng,Z. Xu, X. Chen, X. Ma, Q. Xue, and X. Zhou, NatureMater. , 605 (2013).[24] S. Tan, Y. Zhang, M. Xia, Z. Ye, F. Chen, X. Xie,R. Peng, D. Xu, Q. Fan, H. Xu, J. Jiang, T. Zhang,X. Lai, T. Xiang, J. Hu, B. Xie, and D. Feng, NatureMater. , 634 (2013).[25] Y. Miyata, K. Nakayama, K. Sugawara, T. Sato, andT. Takahashi, Nature Mater. , 775 (2015).[26] Z. R. Ye, C. F. Zhang, H. L. Ning, W. Li, L. Chen, T. Jia,M. Hashimoto, D. H. Lu, Z.-X. Shen, and Y. Zhang, “Si-multaneous emergence of superconductivity, inter-pocketscattering and nematic fluctuation in potassium-coatedFeSe superconductor,” (2015), arXiv:1512.02526.[27] C. H. P. Wen, H. C. Xu, C. Chen, Z. C. Huang, X. Lou,Y. J. Pu, Q. Song, B. P. Xie, M. Abdel-Hafiez, D. A.CHareev, A. N. Vasiliev, R. Peng, and D. L. Feng, Na-ture Commun. , 10840 (2016).[28] F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W.Huang, P. M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu,D.-C. Yan, and M.-K. Wu, Proceedings of the NationalAcademy of Sciences , 14262 (2008).[29] C. Fang, Y.-L. Wu, R. Thomale, B. A. Bernevig, andJ. Hu, Phys. Rev. X , 011009 (2011).[30] T. A. Maier, S. Graser, P. J. Hirschfeld, and D. J.Scalapino, Phys. Rev. B , 100515 (2011).[31] F. Wang, F. Yang, M. Gao, Z. Lu, T. Xiang, and D. Lee,EPL , 57003 (2011).[32] I. I. Mazin, Phys. Rev. B , 024529 (2011).[33] M. Khodas and A. V. Chubukov, Phys. Rev. Lett. ,247003 (2012).[34] D. Guterding, H. O. Jeschke, P. J. Hirschfeld, and R. Va-lent´ı, Phys. Rev. B , 041112 (2015).[35] E. M. Nica, R. Yu, and Q. Si, “Orbital selectivity andemergent superconducting state from quasi-degenerate s -and d -wave pairing channels in iron-based superconduc-tors,” (2015), arXiv:1505.04170.[36] J. T. Park, G. Friemel, Y. Li, J.-H. Kim, V. Tsurkan,J. Deisenhofer, H.-A. Krug von Nidda, A. Loidl,A. Ivanov, B. Keimer, and D. S. Inosov, Phys. Rev.Lett. , 177005 (2011).[37] A. E. Taylor, R. A. Ewings, T. G. Perring, J. S. White,P. Babkevich, A. Krzton-Maziopa, E. Pomjakushina,K. Conder, and A. T. Boothroyd, Phys. Rev. B ,094528 (2012).[38] G. Friemel, W. P. Liu, E. A. Goremychkin, L. Y., J. T.Park, O. Sobolev, C. T. Lin, B. Keimer, and D. S. Inosov,EPL , 67004 (2012).[39] Q. Fan, W. H. Zhang, X. Liu, Y. J. Yan, M. Q. Ren,R. Peng, H. C. Xu, B. P. Xie, J. P. Hu, T. Zhang, andD. L. Feng, Nature Phys. , 946 (2015).[40] Z. Wang, Y. J. Song, H. L. Shi, Z. W. Wang, Z. Chen, H. F. Tian, G. F. Chen, J. G. Guo, H. X. Yang, andJ. Q. Li, Phys. Rev. B , 140505 (2011).[41] W. Li, H. Ding, Z. Li, P. Deng, K. Chang, K. He, S. Ji,L. Wang, X. Ma, J.-P. Hu, X. Chen, and Q.-K. Xue,Phys. Rev. Lett. , 057003 (2012).[42] J. J. Lee, F. T. Schmitt, R. G. Moore, S. Johnston, Y. T.Cui, W. Li, M. Yi, Z. K. Liu, M. Hashimoto, Y. Zhang,D. H. Lu, T. P. Devereaux, D. H. Lee, and Z. X. Shen,Nature , 245 (2014).[43] Z. Li, F. Wang, H. Yao, and D. Lee, Sci. Bull. , 925(2016).[44] X. Dong, K. Jin, D. Yuan, H. Zhou, J. Yuan, Y. Huang,W. Hua, J. Sun, P. Zheng, W. Hu, Y. Mao, M. Ma,G. Zhang, F. Zhou, and Z. Zhao, Phys. Rev. B ,064515 (2015).[45] G. Yu, Y. Li, E. M. Motoyama, and M. Greven, NaturePhys. .[46] Z. Du, X. Yang, H. Lin, D. Fang, G. Du, J. Xing, H. Yang,X. Zhu, and H. Wen, Nature Commun. , 10565 (2016).[47] N. R. Davies, M. C. Rahn, H. C. Walker, R. A. Ewings,D. N. Woodruff, S. J. Clarke, and A. T. Boothroyd,Phys. Rev. B , 144503 (2016).[48] B. Pan, Y. Shen, D. Hu, Y. Feng, J. T. Park,A. D. Christianson, Q. Wang, Y. Hao, H. Wo,and J. Zhao, “Structure of spin excitations in heav-ily electron-doped Li . Fe . ODFeSe superconductors,”(2016), arXiv:1608.01204.[49] J. T. Park, D. S. Inosov, A. Yaresko, S. Graser, D. L.Sun, P. Bourges, Y. Sidis, Y. Li, J.-H. Kim, D. Haug,A. Ivanov, K. Hradil, A. Schneidewind, P. Link, E. Faul-haber, I. Glavatskyy, C. T. Lin, B. Keimer, andV. Hinkov, Phys. Rev. B , 134503 (2010).[50] G. Friemel, J. T. Park, T. A. Maier, V. Tsurkan,Y. Li, J. Deisenhofer, H.-A. Krug von Nidda, A. Loidl,A. Ivanov, B. Keimer, and D. S. Inosov, Phys. Rev. B , 140511 (2012).[51] Y. Zhang, Z. R. Ye, Q. Q. Ge, F. Chen, J. Jiang, M. Xu,B. P. Xie, and D. L. Feng, Nature Phys. .[52] S. Pailh`es, Y. Sidis, P. Bourges, C. Ulrich, V. Hinkov,L. P. Regnault, A. Ivanov, B. Liang, C. T. Lin, C. Bern-hard, and B. Keimer, Phys. Rev. Lett. , 237002 (2003).[53] L. Capogna, B. Fauqu´e, Y. Sidis, C. Ulrich, P. Bourges,S. Pailh`es, A. Ivanov, J. L. Tallon, B. Liang, C. T. Lin,A. I. Rykov, and B. Keimer, Phys. Rev. B , 060502(2007).[54] C. Zhang, R. Yu, Y. Su, Y. Song, M. Wang, G. Tan,T. Egami, J. A. Fernandez-Baca, E. Faulhaber, Q. Si,and P. Dai, Phys. Rev. Lett. , 207002 (2013).[55] P. Steffens, C. H. Lee, N. Qureshi, K. Kihou, A. Iyo,H. Eisaki, and M. Braden, Phys. Rev. Lett. , 137001(2013).[56] S. Onari, H. Kontani, and M. Sato, Phys. Rev. B ,060504 (2010).[57] Q. Wang, J. T. Park, Y. Feng, Y. Shen, Y. Hao, B. Pan,J. W. Lynn, A. Ivanov, S. Chi, M. Matsuda, H. Cao, R. J.Birgeneau, D. V. Efremov, and J. Zhao, Phys. Rev. Lett.116