Neutron scattering is used to probe magnetic excitations in
FeSe_{0.4}Te_{0.6} (T_c=14 K). Low energy spin fluctuations are found with a
characteristic wave vector $(0.5,0.5,L)$ that corresponds to Fermi surface
nesting and differs from Q_m=(\delta,0,0.5) for magnetic ordering in
Fe_{1+y}Te. A spin resonance with \hbar\Omega_0=6.5 meV \approx 5.3 k_BT_c and
\hbar\Gamma=1.25 meV develops in the superconducting state from a normal state
continuum. We show that the resonance is consistent with a bound state
associated with s+/- superconductivity and imperfect quasi-2D Fermi surface
nesting.Comment: 4 pages, 4 figures, Submitted to Phys. Rev. Let

Bin Qian

C. Wang

Collin Broholm

H. H. Wen

Jin Hu

Minghu Fang

S. Chang

V. Stanev

Wei Bao

Y. C. Gasparovic

Y. Zhao

Yiming Qiu

Z. Tesanovic

Z. A. Ren

Zhiqiang Mao

English

arXiv

Neutron scattering is used to probe magnetic excitations in FeSe0.4Te0.6 (Tc = 14 K). Low energy spin fluctuations are found with a characteristic wave vector (1212L) that corresponds to Fermi surface nesting and differs from Qm = (δ012) for magnetic ordering in Fe1+yTe. A spin resonance with ℎΩ0 = 6.51(4) meV ≈ 5.3kBTc and ℎΓ = 1.25(5) meV develops in the superconducting state from a normal state continuum. We show that the resonance is consistent with a bound state associated with s± superconductivity and imperfect quasi-2D Fermi surface nesting

Qiu, Yiming

Bao, Wei

Zhao, Y.

Broholm, Collin

Stanev, V.

Tesanovic, Z.

Gasparovic, Y. C.

Chang, S.

Hu, Jin

Qian, Bin

Fang, Minghu

Mao, Zhiqiang

Johns Hopkins University

Spin gap and resonance at the nesting wave vector in superconducting FeSe0.4Te0.6

JScholarship (Johns Hopkins Univ.)

Spin Gap and Resonance at the Nesting Wave Vector in Superconducting FeSe0:4Te0:6Yiming Qiu,1,2 Wei Bao,3,* Y. Zhao,4 Collin Broholm,4,1 V. Stanev,4 Z. Tesanovic,4 Y. C. Gasparovic,1,2 S. Chang,1Jin Hu,5 Bin Qian,5 Minghu Fang,5,6 and Zhiqiang Mao51NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA2Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA3Department of Physics, Renmin University of China, Beijing 100872, China4Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University,Baltimore, Maryland 21218 USA5Department of Physics, Tulane University, New Orleans, Louisiana 70118 USA6Department of Physics, Zhejiang University, Hangzhou 310027, China(Received 12 May 2009; published 7 August 2009)Neutron scattering is used to probe magnetic excitations in FeSe0:4Te0:6 (Tc ¼ 14 K). Low energy spinfluctuations are found with a characteristic wave vector ( 1212L) that corresponds to Fermi surface nestingand differs from Qm ¼ ð0 12Þ for magnetic ordering in Fe1þyTe. A spin resonance with @0 ¼6:51ð4Þ meV  5:3kBTc and @ ¼ 1:25ð5Þ meV develops in the superconducting state from a normalstate continuum. We show that the resonance is consistent with a bound state associated with ssuperconductivity and imperfect quasi-2D Fermi surface nesting.DOI: 10.1103/PhysRevLett.103.067008 PACS numbers: 74.70.b, 74.20.Mn, 74.25.Ha, 78.70.NxThe recent discovery of superconductivity in oxypnic-tides of the form RFeAsO (1111) [1] has triggered a burstof scientific activity. Subsequently reported superconduc-tivity in suitably doped BaFe2As2 (122) [2], LiFeAs [3],and FeSe (11) [4] indicates a crucial role for the sharedFeAs or FeSe antifluorite layer. The theoretical electronicstructure is indeed dominated at the Fermi level by con-tributions from this layer [5] and density functional theory[6] successfully predicts, as a consequence of Fermi sur-face nesting, the observed antiferromagnetic order in the1111 [7] and 122 type parent compounds [8,9]. In contrast,the magnetic parent compounds of 11-type superconduc-tors order with a tunable antiferromagnetic vector Qm ¼ð0 12Þ [10], with an in-plane component that is rotated by45 with respect to the Qn ¼ ð12 12Þ nesting vector connect-ing the  and M points [see inset to Fig. 1(d)].Recently, a spin resonance was discovered at the anti-ferromagnetic nesting vector in BaFe2As2-derived super-conductors [11–13]. This raises several importantquestions: Does a spin resonance generally exist for theiron pnictide superconductor and for Fe(Se,Te) in particu-lar, where in reciprocal space is it to be found? In thisLetter we report that superconducting Fe(Se,Te) does ex-hibit a spin resonance though not at Qm but at the MFermi surface nesting vector,Qn. This indicates a commonform of superconductivity in the 122 and 11 families ofiron based superconductors and brings into view a strikingunifying feature of a wide range of unconventional super-conductors proximate to magnetism: They exhibit a spinresonance at an energy @0 that scales with kBTc [14] anda commensurate wave vector that reverses the sign of thesuperconducting order parameter.Single crystals of FeSe0:4Te0:6 were grown by a fluxmethod. Growth methods and bulk properties are reportedelsewhere [15]. Bulk superconductivity in samples pre-pared as ours and labeled SC1 in Ref. [15] is indicatedby sharp anomalies in resistivity, magnetic susceptibilityand heat capacity with an onset at Tc  14 K. While thepresent experiment did not probe elastic magnetic scatter-ing, there are no indications of a separate magnetic phasetransition in bulk properties. The lattice parameters of thetetragonal P4=nmm unit cell are a ¼ b ¼ 3:802 A andFIG. 1 (color). Spin excitation spectrum as a function of Q ¼ðH;H;1:2Þ and energy at (a) 1.5 K and (b) 30 K. (c) Thedifference between the 1.5 K and 30 K spectra. The intensity in(c) is multiplied by a factor of 2 so that the same intensity scaleat the top is used for (a)–(c). (d) Resolution convolved theoreti-cal intensity difference from a simplified two-band model ex-tracted from ARPES measurements [25]. The insets show theresolution free theoretical intensity difference (left) and thenormal state Fermi surface employed (right).PRL 103, 067008 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending7 AUGUST 20090031-9007=09=103(6)=067008(4) 067008-1  2009 The American Physical Societyc ¼ 6:061 A at room temperature. Five crystals, weighing2 g each, were mutually aligned to increase the countrate. The mosaic full width at half maximum (FWHM) ofthe individual samples and the coaligned assembly are 2.8degrees and 4.8 degrees, respectively. Magnetic neutronscattering measurements were performed using thermal(BT7) and cold (SPINS) neutron triple-axis spectrometersat NIST. The sample temperature was controlled by apumped 4He cryostat. As opposed to experiments onsamples containing 8% excess Fe [10], no low energymagnetic signals were detected at the antiferromagneticwave vector Qm ¼ ð0 12Þ in FeSe0:4Te0:6. Therefore, wewill concentrate on results from scans in the (HHL) recip-rocal plane from BT7, using the fixed Ef ¼ 14:7 meVconfiguration. Measurements with better resolution andin a 7 T cryomagnet were conducted at SPINS using Ef ¼4:2 meV. Pyrolytic graphite (PG) and cooled Be were usedto reject order contamination on BT7 and SPINS, respec-tively, and both instruments employ PG to monochromatethe incident beam and analyze the scattered beam.Figures 1(a) and 1(b) show the spin excitation spectrumof FeSe0:4Te0:6, combining 10 different constant energyscans near the in-plane nesting vector ( 1212 ), at temperatureT ¼ 1:5 K and 30 K, respectively. The temperature inde-pendent, sharp spurions in (a) and (b) cancel in the differ-ence spectrum [Fig. 1(c)]. An intense ‘‘resonance’’ sharplydefined both in energy and in-plane momentum appearsbelow Tc, above the normal state ridgelike continuum atthe nesting vector Qn rather than at the wave vector Qm ofthe antiferromagnetic parent compound. Correspondinglywe note that while the ‘‘parent’’ nonsuperconducting heavyfermion compound CeRhIn5 orders in an incommensurateantiferromagnetic structure [16], the resonance in super-conducting CeCoIn5 appears at the commensurate wavevector associated with dx2y2 superconductivity [17].Figure 2(a) shows constant-Q scans through the reso-nance above and below Tc, together with measured back-ground. The spectrum appears to be gapless in the normalstate as measured at 30 K with a weak ‘‘knee’’ at theresonance energy. The normal state data in Fig. 1(b) issimilar to data from paramagnetic and metallic V2O3 (seeFig. 2(b) of Ref. [18]) indicating spin fluctuations resultingfrom Fermi surface nesting. At 1.5 K, a full spin gap isopened at low energies as spectral weight concentrates in aresonance peak at @0 ¼ 6:51ð4Þ meV. Higher resolutionconstant-Q scans measured using cold neutrons are shownin Fig. 2(b). Here the SPINS spectrometer was arranged sothe line of intensity from Q ¼ ð0:5; 0:5;0:796Þ to (0.5,0.5,1:804) was collected by the focusing analyzer duringthe scan. The resonance peak is much wider than theFWHM instrumental resolution, 0.48 meV. Theresolution-corrected half width @ ¼ 1:25ð5Þ meV mayindicate a finite lifetime of the resonant spin fluctuations,imperfect nesting, or broadening due to disorder on theSe=Te site.To determine the spatial correlations associated withthe resonance, constant energy scans were performed inits vicinity. Figure 3(a) shows a basal plane scan at theresonance energy covering a full Brillouin zone. Weakintensity atQ ¼ ð12 12 12Þ and T ¼ 30 K is strongly enhancedin the superconducting state at T ¼ 1:5 K. The net en-hancement is shown by the difference data in Fig. 3(c).Spurions exist at both temperatures but these cancel in thedifference plot. The horizontal bar indicates the FWHMinstrumental resolution. Based on the calculated resolu-tion function, the deconvolved half width at half maximumis 0:023ð5Þ  ffiffiffi2p  a, indicating a correlation length of19(4) Å or 7(1) Fe-Fe lattice spacings. Figure 3(b) showsa scan in the interplane direction above and below Tc,with the difference in (d). As for quasi-two-dimensionalBaFe1:84Co0:16As2 [12] but distinct from the more three-dimensional case of BaFe1:9Ni0:1As2 [13], the resonantspin correlations show no Q  c dependence beyond thatassociated with the product of the Fe magnetic form factorsquared and the varying projection of the instrumentalresolution volume along c (solid line).Figure 4 shows the @! T dependence of magneticscattering at the nesting vector. The spin resonance andthe associated spin gap appear along with superconductiv-ity for T < Tc ¼ 14 K. There is no detectable softening ofFIG. 2 (color online). (a) ConstantQ ¼ ð0:46; 0:46; 0:65Þ scanat 1.5 K and 30 K, measured at BT7. The sample-turnedbackground measured at 30 K is shown by green open circles.(b) The difference intensity of the const-Q ¼ ð12 12LÞ scans mea-sured at 4.2 and 30 K using SPINS, with and without an applied7 T magnetic field. The solid line is a guide to the eye. The bluebar indicates the FWHM instrumental energy resolution.PRL 103, 067008 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending7 AUGUST 2009067008-2the resonance energy upon heating, indicating that it re-mains a characteristic energy scale in the normal statespectrum. In the inset, the temperature dependence of theintegrated intensity of the resonance resembles an orderparameter for the superconducting transition as in uncon-ventional cuprate [19] and heavy fermion [17,20] super-conductors. The ratio between the resonance energy andthe superconducting transition temperature @0=kBTc ¼5:3 for our FeSe0:4Te0:6 sample is larger than 2–4 reportedfor heavy fermion superconductors [17,20], 4.3 forBa0:6K0:4Fe2As2 [11] and 4.5 for BaFe1:84Co0:16As2 [12],but comparable to the canonical value of 5 for cupratesuperconductors [21]. It also follows a general trend for awide range of quantum condensation phenomena [14].Turning now to the theoretical interpretation of the data,we note that the Q and E dependent 00ðQ; EÞ measuredthrough magnetic neutron scattering in the superconduct-ing state reflects the symmetry of the superconducting gapfunction [22]. Because of the emblematic s coherencefactors for the interband processes, 1þ 2E2q, the creation ofa pair of Bogoliubov–de Gennes (BdG) quasiparticles isenhanced, in contrast to being suppressed as in a conven-tional s-wave state, where the corresponding coherencefactor is 1 2E2q[23]. This leads to a divergence in theimaginary part of 0ðQn; E ! 2Þ [24]. In addition, inter-actions pull the resonant peak below 2, creating a ‘‘boundstate’’ of two BdG quasiparticles within the superconduct-ing gap.We now demonstrate that this rather simple theoreticalpicture is consistent with the present data. The explicitcalculation employs an RPA-type scheme and uses atwo-band model, with one hole and one electron parabolic2D bands [inset to Fig. 1(d)]. The band parameters are fromARPES measurements [25]. The position of the resonancepeak is mainly controlled by the strength of the interactionwhile the eccentricity determines its width in Q—extract-ing those parameters from the fits is a well-defined proce-dure. Here we use 20 ¼ 7:5 meV (20=kBTc  6:1),higher than the BCS value but within the range measuredin pnictides [26]. The eccentricity of the electron band isaround 0.83, the interaction strength is set to 0.3 in units ofinverse density of states (DOS), and areas of the hole andthe electron pockets are roughly similar. More generally,reasonable fits are obtained for eccentricity and interactionin the ranges 0.83–0.90 and 0.26–0.34, respectively.Following the standard procedure, a small fixed imaginarypart (0:10) was added to! to smooth out the numerics.For comparison to Fig. 1(c) we subtracted the theoretical30 K normal state intensity and convolved with the instru-mental resolution. The result captures the essential physicsof the resonance, as shown in Fig. 1(d).The main insight gained by this calculation is that thegood fit to the observed shape and position of the resonancenecessarily calls for significant deviations from perfectnesting. In agreement with the ARPES data, we find bestfits for a circular hole band and an elliptical electron band.This explains the absence of an antiferromagnetic spin-density-wave (SDW) ordering along the ‘‘nesting’’ vectorin the normal state [10]—the peak in the spin susceptibilityis highly sensitive to deviations from perfect nesting [27]FIG. 4 (color). The energy scan at Q ¼ ð0:46; 0:46; 0:66Þ as afunction of temperature indicating association between the spinresonance and superconductivity in FeSe0:4Te0:6. The sample-turned background was subtracted from the data. The insetshows the integrated intensity of the resonance between5 meV and 8 meV as a function of temperature, and the line isa fit to mean field theory with Tc ¼ 14 K.FIG. 3 (color online). Constant @! ¼ 6:5 meV scans(a) along the (HH 12 ) direction, and (b) along the (1212L) direc-tion, showing the quasi-two-dimensionality of the spin reso-nance. (c)–(d) The difference between the 1.5 K and 30 Kscans. In (c) the solid line is a fit to a resolution convolvedLorentzian, and the horizontal bar represents the FWHM of theresolution. In (d) the line is the product of the Fe magnetic formfactor squared and the projection of the instrumental resolutionvolume along c.PRL 103, 067008 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending7 AUGUST 2009067008-3and the combination of a depressed peak and better-screened interactions can readily destabilize the SDWstate. Overall, the above calculation supports the s super-conducting state and the notion that superconductivity setsin after the itinerant SDW order has been suppressed bydeviations from perfect nesting.Since the discovery of the spin resonance in cupratesuperconductors [19], there has been much debate onwhether it is associated with an intrinsic influence of super-conductivity on spin correlations, or with a pre-existingcollective mode of a nearby magnetic order enhanced bythe loss of electron-hole pair damping in the superconduct-ing state [21]. According to the former scenario and thetheory described above, the resonance should be a triplet—splitting linearly in an applied field. To determine the spinspace multiplicity of the resonance, we carried out aconstant-@! scan in a field of 7 Tesla. No splitting isdirectly visible in the data shown in Fig. 2(b). Fitting thesedata to a triplet (doublet) places an upper limit of 1.3 meV(1.2 meV) on the overall level spacing. For comparison,Zeeman splitting of a spin multiplet with g ¼ 2 wouldamount to gBH ¼ 0:81 meV. Higher fields may help toovercome the zero field broadening and determine themultiplicity of the resonance.In summary, we observe a strong quasi-two-dimensionalspin resonance at the energy @0 ¼ 6:5 meV and the wavevector Qn ¼ ð12 12LÞ in superconducting FeSe0:4Te0:6. Thepeak has finite half widths in momentum and energy of0:06ð1Þ A1 and @ ¼ 1:25ð5Þ meV, respectively. Theseexperimental results are consistent with theoretical predic-tions for a s superconducting pairing function [23,24,27].Despite a different critical wave vector Qm in the antifer-romagnet parent compound Fe1þyTe, imperfect nesting ofhole and electron Fermi surfaces separated by Qn appearsto lie behind s superconductivity in FeSe0:4Te0:6 as in theother Fe-based superconductors.Work at Tulane was supported by the NSF under GrantNo. DMR-0645305 for materials, the DOE under DE-FG02-07ER46358 for graduate students, and by theResearch Corporation. Work at JHU was supported bythe DOE under DE-FG02-08ER46544. Work at ZU wassupported by the NBRP of China (No. 2006CB01003,2009CB929104) and the PCSIRT of the MOE of China(IRT0754). SPINS is in part supported by NSF underagreement DMR-0454672.Note added.—After completing our experiments atBT7 and SPINS on March 9, 2009, a related preprintdescribing neutron scattering experiments on a mixtureof FeSe0:45Te0:55 and FeSe0:65Te0:35 came to our attention[28].*wbao@ruc.edu.cn[1] Y. Kamihara et al., J. Am. Chem. Soc. 130, 3296 (2008);X. H. Chen et al., Nature (London) 453, 761 (2008); G. F.Chen et al., Phys. Rev. Lett. 100, 247002 (2008); Z. A.Ren et al., Chin. Phys. Lett. 25, 2215 (2008); H. H. Wenet al., Europhys. Lett. 82 17 009 (2008); C. Wang et al.,ibid. 83, 67 006 (2008).[2] M. Rotter et al., Phys. Rev. Lett. 101, 107006 (2008);G. F. Chen et al., Chin. Phys. Lett. 25, 3403 (2008);K. Sasmal et al., Phys. Rev. Lett. 101, 107007 (2008);M. S. Torikachvili et al., ibid. 101, 057006 (2008);G. Wu et al. Europhys. Lett. 84, 27 010 (2008).[3] X. Wang et al., Solid State Commun. 148, 538 (2008);J. H. Tapp et al., Phys. Rev. B 78, 060505(R) (2008);M. J. Pitcher et al., Chem. Commun. (Cambridge) 45(2008) 5918.[4] F.-C. Hsu et al., Proc. Natl. Acad. Sci. U.S.A. 105, 14 262(2008); M.H. Fang et al., Phys. Rev. B 78, 224503(2008).[5] D. J. Singh, Physica (Amsterdam) 469C , 418 (2009).[6] F. Ma and Z.Y. Lu, Phys. Rev. B 78, 033111 (2008);J. Dong et al., Europhys. Lett. 83, 27 006 (2008).[7] C. de la Cruz et al., Nature (London) 453, 899(2008); M.A. McGuire et al., Phys. Rev. B 78, 094517(2008)[8] Q. Huang et al., Phys. Rev. Lett. 101, 257003 (2008).[9] A. Goldman et al., Phys. Rev. B 78, 100506(R) (2008).[10] W. Bao et al., Phys. Rev. Lett. 102, 247001 (2009).[11] A. D. Christianson et al., Nature (London) 456, 930(2008).[12] M.D. Lumsden et al., Phys. Rev. Lett. 102, 107005(2009).[13] S. Chi et al., Phys. Rev. Lett. 102, 107006 (2009); S. Liet al., Phys. Rev. B 79, 174527 (2009).[14] Y. J. Uemura, Nature Mater. 8, 253 (2009).[15] T. Liu et al., arXiv:0904.0824.[16] W. Bao et al., Phys. Rev. B 62, R14621 (2000); 67, 099903(E) (2003).[17] C. Stock et al., Phys. Rev. Lett. 100, 087001 (2008).[18] W. Bao et al., Phys. Rev. Lett. 78, 507 (1997).[19] J. Rossat-Mignod et al., Physica (Amsterdam) 185–189C,86 (1991); H. A. Mook et al., Phys. Rev. Lett. 70, 3490(1993); H. F. Fong et al., Nature (London) 398, 588(1999); H. F. He et al., Science 295, 1045 (2002).[20] N. Metoki et al., Phys. Rev. Lett. 80, 5417 (1998);O. Stockert et al., Physica (Amsterdam) 403B, 973 (2008).[21] P. Bourges et al., Physica (Amsterdam) 424C, 45 (2005).[22] R. Joynt and T.M. Rice, Phys. Rev. B 38, 2345 (1988).[23] I. I. Mazin and J. Schmalian, Physica (Amsterdam) 469C,614 (2009).[24] M.M. Korshunov and I. Eremin, Phys. Rev. B 78, 140509(R) (2008); T. Maier and D. Scalapino, ibid. 78, 020514(R) (2008).[25] Y. Xia et al., Phys. Rev. Lett. 103, 037002 (2009).[26] L. Zhao et al., Chin. Phys. Lett. 25, 4402 (2008); H. Dinget al., Europhys. Lett. 83, 47001 (2008).[27] V. Cvetkovic and Z. Tesanovic, Europhys. Lett. 85, 37002(2009).[28] H. A. Mook et al., arXiv:0904.2178.PRL 103, 067008 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending7 AUGUST 2009067008-4

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Spin Gap and Resonance at the Nesting Wave Vector in Superconducting
                    
                      
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Spin Gap and Resonance at the Nesting Wavevector in Superconducting
  FeSe0.4Te0.6

Spin Gap and Resonance at the Nesting Wavevector in Superconducting FeSe0.4Te0.6

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