(π,0) antiferromagnetic spin excitations in superconducting Rb Fe Se 0.82 1.68 2 Miaoyin Wang,1 Chunhong Li,2 D. L. Abernathy,3 Yu Song,1 Scott V. Carr,1 Xingye Lu,2,1 Shiliang Li,2 Jiangping Hu,4,2 Tao Xiang,2 and Pengcheng Dai1,2,∗ 1Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA 2Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, P. O. Box 603, Beijing 100190, China 3Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA 4Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA We use inelastic neutron scattering to show that superconducting (SC) rubidium iron selenide 2 Rb0.82Fe1.68Se2 exhibits antiferromagnetic (AF) spin excitations near the in-plane wave vector 1 Q = (π,0) identical to that for iron arsenide superconductors. Moreover, we find that these ex- 0 citations change from incommensurate to commensu√rate w√ith increasing energy, and occur at the 2 expenseofspinwavesassociatedwiththecoexisting 5× 5blockAFphase. Sinceangleresolved photoemissionexperimentsrevealnoevidenceforhole-likeFermisurfaceatΓ(0,0),ourresultssug- n gest that the Q = (π,0) excitations in SC Rb Fe Se come from localized moments and may a 0.82 1.68 2 have a similar origin as the hourglass-like spin excitations in copper oxide superconductors. J 6 1 Introduction The family of alkaline iron selenide superconductors A Fe Se (A = K, Rb, Cs) [1–4] has y 1.6+x 2 generated considerable interest because superconductivity in these materials may have a different origin from the ] n sign reversed s-wave electron pairing mechanism [5–7], a leading candidate for superconductivity in iron pnictide o superconductors [8]. Although A Fe Se materials are isostructural with the metallic iron pnictides such as y 1.6+x 2 √ √ c (Ba,Ca,Sr)Fe As [9], they are insulators near x=0 [3, 4] and form a 5× 5 block AF structure with Fe vacancy - 2 2 r order(Fig. 1a)[10–14]completelydifferentfromthecollinearAFstructureoftheironpnictides[15]. Sincesupercon- p ductivityinA Fe Se alwaysappearsconcurrentlywiththeblockAForder[11–14], whereasintheironpnictides u y 1.6+x 2 s superconductivity arises at the expense of the static AF order [15], it is important to determine the relationship . between superconductivity and magnetism in these materials. Although experiments using transmission electron mi- t a croscopy[16],X-raydiffraction[17],muon-spinrotation(µSR)[18],scanningtunnelingmicroscopy[19],angleresolved m photoemission(ARPES)[20],M¨ossbauer[21],andoptical[22,23]spectroscopyhaveprovidedtantalizingevidencefor - several coexisting phases in superconducting (SC) AFe Se , it is still unclear what is the exact crystal structure d 1.6+x √2 √ n and stoichiometry of the SC phase and its relationship to the 5× 5 AF phase. o Forironpnictides[9],bandstructurecalculationshavepredictedthatFermisurfacesofthesematerialsarecomposed c of hole and electron pockets near Γ(0,0) and M(π,0)/M(0,π) points, respectively [8]. Since antiferromagnetism and [ superconductivity can arise from the sign reversed quasiparticle excitations between the hole and electron pockets 1 [8], there should be a neutron spin resonance at the in-plane wave vector Q = (π,0) [24, 25]. Indeed, inelastic v neutron scattering experiments on single crystals of electron and hole-doped BaFe As have found the resonance at 2 2 8 Q = (π,0) [26–29] and thus provided evidence for the electron s±-wave pairing mechanism [8]. In the case of SC 4 A Fe Se , since ARPES measurements [5–7] found electron Fermi surfaces at the M(π,0)/M(0,π) points but no 3 y 1.6+x 2 3 hole Fermi surface near Γ(0,0), quasiparticle excitations between Γ(0,0) and M(π,0)/M(0,π) should not provide AF . spinexcitationsatQ=(π,0)(Fig. 1c). Instead,thenestingpropertiesbetweentheM(π,0)/M(0,π)electronpockets 1 in a d-wave symmetry is expected to give a broad plateau like maximum around Q=(π,π) that is bordered by two 0 2 peaks at Q ≈ (π,0.625π) and Q ≈ (0.625π,π) [30]. Although the recent discovery of the neutron spin resonance in 1 SC Rb Fe Se at wave vectors Q = (±π,±0.5π) [or Q = (±0.5π,±π)] (Fig. 1d) [31, 32] is consistent with this y 1.6+x 2 v: picture [30], it remains unknown whether there are spin excitations at other wave vectors not associated with the i Fermi surface nesting. X InthisLetter,weuseneutronscatteringtomapoutthelow-energyspinexcitationsinSCRb Fe Se (T =32 0.82 1.68 2 c r K, Fig. 1f). In addition to confirming the neutron spin resonance at Q=(±π,±0.5π) [31, 32], we find clear evidence a for incommensurate spin excitations near wave vector Q=(π,0) that are absent in insulating Rb Fe Se (Figs. 0.89 1.58 2 1b and 1d) [33]. With increasing energy, the incommensurate spin excitions disperse inward to Q = (π,0) and disappear above E =30 meV (Figs. 2,3). A comparison of spin excitations in SC Rb Fe Se with spin waves in 0.82 1.68 2 insulating Rb Fe Se [33] reveals that the intensity gain of the Q = (π,0) excitations is at the expense of spin 0.89 1.58 2√ √ waves associated with the 5× 5 AF phase (Fig. 3). Since electron-hole pocket excitations are impossible between Γ(0,0) and M(π,0)/M(0,π) points [5–7], our results suggest the presence of local moments [34] in addition to the itinerant electron induced resonance [31, 32]. Moreover, the dispersion of the Q=(π,0) excitations is similar to that of copper oxide superconductors [35, 36] and insulating cobalt oxide [37], thus suggesting the possible presence of dynamic stripes [38]. 2 √ √ FIG. 1: (Color online) (a) The block antiferromagnetic spin structure of the insulating A Fe Se , where the 5× 5 y 1.6+x 2 superlattice structure is marked as grey with lattice parameter a =8.663 ˚A and the orthorhombic lattice cell similar to iron s pnictidesisshadedgreen[33]. (b)Thereciprocalspaceinthe[H ,K ]plane,wherethesolidredcirclesindicatetheAFBragg o o peak positions. (c) Schematics of the Fermi surfaces of SC A Fe Se from ARPES measurements. There are four large y 1.6+x 2 electron pockets at Q = (±1,0)/(0,±1) and a small electron pocket at Γ(0,0) [5–7]. The neutron spin resonance is believed to originate from the electron-electron pocket excitations as shown by the red arrows [31, 32]. The green arrow indicates the Γ ↔ M transition. (d) Positions of observed spin excitations in SC Rb Fe Se , where spin waves from the block 0.82 1.68 2 AF phase, neutron spin resonance, and (π,0) excitations are marked as red solid circles, purple ellipses and light-blue cross shapes, respectively. (e) Integrated intensity comparison of several samples at E = 14±2 meV. Olive Green: spin waves in the insulating Rb Fe Se ; Dark red, light blue, and light violet are spin waves, (π,0) excitations, and resonance in SC 0.89 1.58 2 Rb Fe Se ; Orange: spin wave in BaFe As . (f) Susceptibility measurement indicates T =32 K. 0.82 1.68 2 2 2 c Results We have performed inelastic neutron scattering experiments on the ARCS chopper spectrometer at the SpallationNeutronSource, OakRidgeNationalLaboratoryusingidenticalconditionsaspreviousworkonspinwaves √ √ in insulating Rb Fe Se [33]. Figures 1a and 1b show the 5× 5 block AF structure and the positions of 0.89 1.58 2 the AF peaks in reciprocal space, respectively [33]. We define the wave vector Q at (q ,q ,q ) as (H ,K ,L ) = x y z o o o (q a /2π,q a /2π,q c /2π) rlu, where a = 5.48 and c = 14.69 ˚A are the orthorhombic cell lattice parameters x o y o z o o o similar to iron pnictides [39]. In this notation, the neutron spin resonance [31, 32] occurs at Q = (±1,±0.5) [or Q = (±π,±0.5π)] (Fig. 1d), while the Γ ↔ M Fermi surface nesting gives scattering at Q = (±1,0) rlu (Figs. 1c and1d). Weco-aligned∼6gramsoftheSCsinglecrystalsRb Fe Se grownbyself-fluxmethod(withmosaicof 0.82 1.68 2 ∼6◦) [33], where the chemical composition was determined by inductively-coupled plasma analysis. Figure 1f shows the temperature dependence of the susceptibility measurements confirming T = 32 K. To ensure that the neutron c spin resonance at Q = (−1,0.5) at E = 14 meV [31, 32] does not fall into detector gaps on ARCS, we rotated the co-aligned samples counter-clockwise by ∼27 degrees. The incident beam energies were E = 35,80 meV with E i i parallel to the c-axis. The scattering intensities were normalized to absolute units using a vanadium standard and can therefore be compared directly with spin waves in insulating Rb Fe Se [33]. 0.89 1.58 2 From earlier work on A Fe Se [11–14], we know that superconductivity coexists with the block AF order. y 1.6+x 2 Therefore, one should expect acoustic spin waves in SC Rb Fe Se from the block AF phase [33]. Figure 2 0.82 1.68 2 summarizes the two-dimensional constant-energy (E) images of spin excitations in the [H ,K ] plane for insulating o o and SC Rb Fe Se . Since the subtle changes in the insulating and SC samples [11–14] are not expected to much y 1.6+x 2 affect phonons in these materials, we assume that the new dispersive features in Rb Fe Se are spin excitations 0.82 1.68 2 associated with the SC phase. Figures 2a-2d show images of acoustic spin waves at energies E =8±2, 12±2, 20±2, and26±2meV,respectively,forinsulatingRb Fe Se [33]. Theyarecenteredattheexpectedin-planeAFwave 0.89 1.58 2 3 FIG. 2: (Color online) (a-d) Wave-vector dependence of spin-wave excitations at different energies for NSC Rb Fe Se at 0.89 1.58 2 10 K obtained with incident neutron energy of E = 80 meV [33]. (e-h) Identical images for SC Rb Fe Se at 6 K. The i 0.82 1.68 2 red squares are the Brillouin zone for iron pnictides [39]. (i-l) Expanded view of the excitations near Q=(1,0). The data in (j,k) are collected with E =35 meV, while (i,l) are taken with E =80 meV. The dashed ellipses in (j) mark positions of the i i resonance. The vertical color bars indicate intensity scale in mbarns/sr/meV/f.u. vectors with no observable features at Q=(1,±0.5) and Q=(1,0) [33]. Figures 2e-2h plot images of the identical constant-energy cuts for SC Rb Fe Se at T = 6 K. In addition 0.82 1.68 2 to the usual spin waves from the block AF structure, we find new features near Q = (±1,0) and Q = (0,±1). At E =8±2 meV, there are four incommensurate peaks centered at Q≈(−1±0.14,±0.1) (Fig. 2e). Upon increasing energies to E = 12±2 (Fig. 2f) and 20±2 meV (Fig. 2g), the excitations become approximately centered at Q = (±1,0). Finally at E = 26±2 meV, they disappear at Q = (±1,0) and spin waves in SC Rb Fe Se and 0.82 1.68 2 insulating Rb Fe Se become indistinguishable (Figs. 2d and 2h). Figures 2i-2l show the expanded view of the 0.89 1.58 2 spin excitations near Q = (−1,0) at different energies. At E = 8±2 meV, we see four distinct peaks (Fig. 2i). At the neutron spin resonance energy of E = 12±2 meV, the excitations become cross-like near Q = (−1,0) and one can also see the resonance centered at Q=(−1,±0.5) ( Fig. 2j) [31, 32]. Upon increasing energy to E =16±2 meV, the excitations are well centered at Q=(−1,0) (Fig. 2k). Finally at E =26±2 meV, we find only spin waves from the block AF phase centered around the expected AF positions. To see how the excitations near Q = (1,0) respond to superconductivity and determine whether they are related to spin waves from the block AF phase, we show in Fig. 3 constant-energy cuts for the Q = (1,0) excitations and block AF spin waves at different temperatures. The neutron scattering cross section S(Q,E) is related to the imaginary part of the dynamic susceptibility χ(cid:48)(cid:48)(Q,ω) by correcting for the Bose population factor via S(Q,E) = 1/(1−exp(−E/(k T)))χ(cid:48)(cid:48)(Q,E), where k is the Boltzmann’s constant. Figures 3a-3c show constant-energy cuts B B along the K direction for different temperatures at E =8±2, 12±2, and 16±2 meV, respectively. While χ(cid:48)(cid:48)(Q,ω) o at the probed energies show no appreciable changes across T , it decreases on warming to T =250 K, consistent with c spin excitations. For comparison, we find that χ(cid:48)(cid:48)(Q,ω) of the spin waves from the block AF phase are temperature independentbetween10Kand250K(Figs. 3d-3f). Thisisexpectedsincespinwavesarebosonsandshouldfollowthe BosefactorbelowT . ToseeifsuperconductivityhasanyeffectonspinwavesoftheblockAFphase,weshowinFigs. N 3g-3i χ(cid:48)(cid:48)(Q,ω) for SC Rb Fe Se and insulating Rb Fe Se . While the spin wave intensity at E = 10±2 0.82 1.68 2 0.89 1.58 2 and 20±2 meV in the superconductor are lower than that of the insulator, it becomes similar at E =34±2 meV. To quantitativelycomparethedifferencesbetweentheintensitygainnear(−1,0)withintensitylossoftheAFspinwaves in superconductor compared with that of the insulator, we plot in in Fig. 3j the ratio of yellow area and yellow plus green areas for SC and insulating samples (Fig. 3k) as black square and yellow cirlces, respectively. We see that the 4 FIG.3: Cutsofχ(cid:48)(cid:48)(Q,ω)along(a)the[−0.8±0.1,K],(b,c)[−1±0.1,K]directionsfortheQ=(−1,0)excitationsatdifferent temperatures. (d-f) Cuts of spin waves along the [−0.6±0.1,K] direction at different energies and temperatures reveal that χ(cid:48)(cid:48)(Q,ω) is temperature independent up to T =250 K. (g-i) Comparison of the low-temperature spin wave intensities for SC and insulating samples using the same cuts along the [−0.6±0.1,K] direction. The spin wave intensity of the SC sample are lower at E = 12±2 and 20±2 meV but become similar as that of the insulating sample at E = 34±2 meV. (j) The black squares are ratio of spin waves in yellow area for SC and insulating samples. The yellow circles are the ratio of excitations in yellow area + green area for SC and insulating samples. spin wave intensity loss below ∼30 meV is approximately compensated by an intensity gain from excitations around (−1,0). Finally,toconfirmtheneutronspinresonancenearE =14meVatQ=(−1,0.5)inourSCRb Fe Se [31,32], 0.82 1.68 2 we carried out constant-Q and constant-energy cuts to the data in Fig. 2j below and above T . Figure 4a shows the c S(Q,E) for integrated wave vectors Q = (−0.5±0.1,1±0.1) at 6 K and 35 K. The temperature difference plot (6 K−35 K)in Fig. 4b has a clear peak at E = 14 meV, thus confirming the neutron spin resonance in the SC state [31, 32]. Figures 2c and 2e show constant-energy cuts along the two different high symmetry directions (see insets) below and above T . The temperature difference plots show well-defined peaks at the expected wave vector, again c consistentwithpreviouswork[31,32]. Figure1ecomparesthestrengthofthespinwavesfromtheblockAFstructure in insulating and SC samples, the (1,0) spin excitations, the resonance, and spin waves of BaFe As [39] near E =14 2 2 meV. Discussion The discovery of spin excitations near the (π,0) AF wave vector and their dispersion in SC Rb Fe Se have several important implications. First, since ARPES experiments reveal that SC A Fe Se 0.82 1.68 2 y 1.6+x 2 have no hole-like Fermi surface at Γ(0,0) [5–7], the (π,0) spin excitations cannot arise from quasiparticle excitations between Γ and M points and most likely come from localized magnetic moments [34]. Taking into account that SC Rb Fe Se also has a neutron spin resonance most likely arising from Fermi surface nesting and itinerant 0.82 1.68 2 electrons [31, 32], these results suggest that localized moments and itinerant electrons are both important ingredients for magnetism in alkaline iron selenide superconductors. Second, the observation of low-energy incommensurate spin excitations and its inverse dispersion are reminiscent of the spin excitations for copper oxide superconductors [35, 36] and insulating La Sr CoO [37]. This suggests that the (π,0) spin excitations stem from strongly correlated elec- 2−x x 4 5 FIG. 4: (a) Energy cut at the resonance position by integrating Q = (−0.5±0.1,1±0.1). (b) Subtracting 35 K data from 6 K data shows a resonance at E = 14 meV. The horizontal bar is the instrumental energy resolution. Constant-energy cuts along the (c) [H,1±0.1] and (e) [0.5±0.1,K] directions. The 6 K−35 K data confirm the resonance peak at (1,−0.5) with a width FWHM =0.13±0.04 along the H direction and FWHM =0.20±0.05 along the K direction. tronic physics and may be associated with dynamic stripes [38]. Third, the reduction in the low-energy spin wave intensity for the block AF phase in SC Rb Fe Se and the concurrent appearance of the incommensurate spin 0.82 1.68 2 excitations near Q = (π,0) indicate that spin excitations in superconductors are compensated by spin waves in the AF block phase. If the SC phase in Rb Fe Se mesoscopically coexists with the block AF phase [16–23], one can 0.82 1.68 2 imagine the formation of a striped phase on the interface region of the block AF phase and the SC phase due to the interaction between local moments and itinerant electrons. The latter can be viewed as dopants to a Mott insulator phase and natually result in a stripe phase as in the case of copper oxides [38]. Acknowledgements We thank Qimiao Si for helpful discussions and R. 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