Coupling of spin and orbital excitations in the iron-based superconductor FeSe(0.5)Te(0.5)
S.-H. Lee, Guangyong Xu, W. Ku, J. S. Wen, C. C. Lee, N. Katayama, Z. J. Xu, S. Ji, Z. W. Lin, G. D. Gu, H.-B. Yang, P. D. Johnson, Z.-H. Pan, T. Valla, M. Fujita, T. J. Sato, S. Chang, K. Yamada, J. M. Tranquada
CCoupling of spin and orbital excitations in the iron-based superconductor FeSe . Te . S.-H. Lee, Guangyong Xu, W. Ku, J. S. Wen,
2, 3
C. C. Lee, N. Katayama, Z. J.Xu,
2, 4
S. Ji, Z. W. Lin, G. D. Gu, H.-B. Yang, P. D. Johnson, Z.-H. Pan, T. Valla, M. Fujita, T. J. Sato, S. Chang, K. Yamada, and J. M. Tranquada Department of Physics, University of Virginia, Charlottesville, VA 22904-4714 Condensed Matter Physics & Materials Science Department,Brookhaven National Laboratory, Upton, New York 11973-5000 Department of Materials Science & Engineering,Stony Brook University, Stony Brook, NY 11794 Physics Department, The City College of New York, New York, NY 10031 Institute for Materials Research, Tohoku University, Senda, Miyagi 980-8577, Japan Neutron Science Laboratory, Institute for Solid State Physics,University of Tokyo, 106-1 Shirakata, Tokai, Ibaraki 319-1106, Japan NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899 WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan (Dated: November 2, 2018)We present a combined analysis of neutron scattering and photoemission measurements on su-perconducting FeSe . Te . . The low-energy magnetic excitations disperse only in the directiontransverse to the characteristic wave vector ( , , , ,
0) appears to consist of four incommensurate pockets. While the spin resonance occurs at anincommensurate wave vector compatible with nesting, neither spin-wave nor Fermi-surface-nestingmodels can describe the magnetic dispersion. We propose that a coupling of spin and orbital corre-lations is key to explaining this behavior. If correct, it follows that these nematic fluctuations areinvolved in the resonance and could be relevant to the pairing mechanism.
The quest to understand the mechanism of high tem-perature superconductivity gained new momentum withthe recent discovery of Fe-based superconductors. Ex-perimental studies of these materials have shown that bychemically tuning the carrier density one can obtain bothmagnetically ordered and superconducting phases. Thesuperconducting transition temperature is maximized forconditions close to where magnetic order is suppressed,leading to predictions that magnetic fluctuations areimportant for electron pairing and motivating compar-isons with copper-oxide superconductors. Initial theorieshave treated the magnetic excitations as independent ofthe atomic orbital character of the conduction electronstates, an assumption that seems to work well in othermetallic magnetic systems; however, there have been re-cent proposals that coupled spin and orbital order occurin the antiferromagnetic state.
In this paper, we present a study of low-energymagnetic and electronic excitations in superconductingFeSe . Te . . Particularly striking is the anomalousanisotropic dispersion of magnetic excitations, which isquite distinct from the spin-wave-like excitations typi-cally seen in magnetic metals. Angle-resolved photoemis-sion spectroscopy (ARPES) reveals an unexpected split-ting of larger Fermi-surface pockets into smaller pocketswith distinct orbital characters. A simple nesting picturedoes not appear to be compatible with the magnetic dis-persion. We propose, instead, that a strong coupling ofspin and orbital correlations can lead to the observedanisotropy. Such a coupling would suggest that elec-tronic nematic fluctuations may be present in the nor-mal state and may participate in the superconductivity. This would be a rather different way to connect with thecuprates. Before continuing, let us first resolve our choice of co-ordinates. The structure of FeSe . Te . contains layersof Fe atoms forming a square lattice, with Se/Te atomscentered above or below these squares, alternating ina checkerboard fashion [Fig 1(a)]. The c-axis displace-ments of the Se/Te atoms break the translational sym-metry, doubling the unit cell size; however, as we willshow, this effect is rather weak for the low-energy elec-tronic structure involving Fe-derived orbitals. Hence, wechoose to work with a unit cell containing one Fe atom( a = b = 2 .
69 ˚A and c = 6 .
27 ˚A). Reciprocal latticevectors will be specified in units of (2 π/a, π/a, π/c ).It is already experimentally established that thelow energy magnetic excitations in superconductingFeSe x Te − x occur near the in-plane wave vector Q =( , which is the same as the magnetic ordering wavevector found in R FeAsO ( R = La, Ce, Pr, Nd) and A Fe As ( A = Ca, Sr, Ba), where it corresponds tocolumnar antiferromagnetic order [Fig. 1(b)]. (Note thatthe magnetic ordering in Fe δ Te is different. ) Sev-eral recent theoretical analyses have proposed that or-bital ordering, involving the Fe 3 d xz and 3 d yz states, isan essential feature of the magnetically-ordered state. This is consistent with the fact that a symmetry-loweringstructural transition, which breaks the degeneracy ofthe d xz and d yz states, always occurs before magneticordering. Very recent experiments emphasize the elec-tronic anisotropy of this state, demonstrating its ne-matic character .For the experimental studies, single crystals of a r X i v : . [ c ond - m a t . s up r- c on ] J un FeSe/Te ! XY M (a)(b) (c) HK -0.5 -0.50.5 scan Ascan B (d) FIG. 1: (color online). (a) Atomic positions within an Feplane of FeSe . Te . . Filled (open) diamonds indicate Se/Teatoms that sit above (below) the plane. Solid line: unit cellused here; dashed line: crystallographic unit cell. (b) Spinpattern corresponding to Q = ( , FeSe . Te . were grown at Brookhaven by a unidirec-tional solidification method. The nominal compositionhad no excess Fe, and T c , measured by magnetic sus-ceptibility, is 14 K. The ARPES spectra were recordedon beamline U13UB at the National Synchrotron LightSounce using a Scienta SES2002 electron spectrometer.The incident photon energy was 17 eV, while the photo-electron energy and angular resolution was 15 meV and0.1 ◦ , respectively. Samples (small pieces from the crystalstudied with neutrons) were cleaved in situ (base pressureof 5 × − Torr) and held at T = 15 K for the mea-surements. Complementary ARPES data were collectedon beamline 12.0.1 at the Advanced Light Source (ALS),using 50-eV photons (energy resolution of 25 meV) and T = 15 K.The neutron scattering experiments were performed atthe cold-neutron triple-axis spectrometer SPINS locatedat the National Institute of Standards and TechnologyCenter for Neutron Research (NCNR). The 9-g crystalwas aligned in the ( hk
0) scattering plane; a mosaic widthof < . ◦ (limited by resolution) was measured. Theincident neutron energy was selected with a vertically-focusing pyrolytic graphite (PG) (002) monochromator.Scattered neutrons were analyzed with five 2.1 cm × E f = 5 . He proportional counter.A cooled Be filter was placed between the sample andanalyzer to suppress higher order neutron contamination.Let us consider the ARPES results first. The electronicspectral weight within 0–10 meV of the Fermi energy, E F , B i nd i ng E ne r g y ( m e V ) k x (rlu)(a) (b) Cut A k y (rlu)0.50.0 k y (r l u ) Cut A
M Y M ! X ! E ne r g y ( e V ) k x k y MY X ! (c) (d) E F FIG. 2: (a) ARPES intensity map at E F , integrated over0–10 meV binding energy; upper half measured at the ALSwith 50-eV photons, lower half from the NSLS with 17-eVphotons. Thick red lines indicate estimated Fermi-surface po-sitions; thin red lines denote pockets inferred by symmetry.Red arrows denote polarization direction; at (0 , .
5) polariza-tion has a k z component that varies with k x . (b) Intensitymap (white = minimum, blue = maximum) along line de-noted as Cut A in (a). Red dots indicate positions of bandsas they cross E F . Asymmetry about k y = 0 is due to imper-fect sample orientation. (c) Calculated spectral weight at E F ,averaged over k z . Orbital coding: red– d yz ; blue– d xz ; green–all others. (d) Calculated band dispersions along symmetrydirections, with intensity scaled according to spectral weight,obtained by unfolding bands calculated in a reduced zone ;color code same as (c). is plotted in Fig. 2(a); the positions of identified bandcrossings, determined from energy-momentum cuts as inFig. 2(b), are indicated by thick red lines. For compar-ison, our local density calculation of the Fermi surfaceis shown in Fig. 2(c) and the back-folded band struc-ture in Fig. 2(d). Several features are obvious. First ofall, we can see that the effect of the unit cell doublingdue to the Se/Te positions is small. To appreciate this,note from Fig. 1(c) that for the doubled unit cell the Γand M points correspond to the same crystal momen-tum. While the band dispersions must be the same atboth points, the spectral weights of the individual bandsneed not be, and that is certainly the case here. Indeed,in Fig. 2(d) one can barely recognize the relationship be-tween M and Γ points, reflecting weak Umklapp effectson the Fe-orbitals.Secondly, experiment indicates the presence of small,incommensurate pockets about the X and Y points, incontrast to the larger commensurate pockets predicted byour calculation. The spectral intensities of these pocketsare quite sensitive to the orientation of the photon po-larization. We can understand this dependence as fol-lows. The theoretical pockets about X (and Y) havedistinct orbital character, as indicated in Fig. 2(c) and(d). Fe d yz character (red) dominates near ( , ± k , d xz (blue) near ( ± h , , d xy around ( − h , , , − k, p orbitals, d yz / d xz / d xy Wannier orbitals actuallycontain p x / p y / p z character (see Ref. 6 for a related anal-ysis of Wannier functions). Assuming that the ARPESmatrix elements are primarily p → s (which is reasonablefor low photon energies), the association between orbitalcharacter and polarization direction is: d yz : [100], d xz :[010], d xy : [001]. From the observed intensities, we con-clude that the pockets at ( , ± k ,
0) are d yz -like, those at( ± h , ,
0) are d xz -like, and those at (0 , ± k ,
0) [and,by symmetry, at ( ± h , , d xy -like. The orbitalcharacter of the spectral weight at E F is qualitativelycompatible with calculations. At the same time, theobserved small hole pockets are different from the largerFermi surfaces of the local density calculation, probablydue to the inability of this mean-field technique to prop-erly account for dynamical magnetic correlations.Now let us turn to the neutron scattering results. Asalready mentioned, a spin resonance has been observedto develop below T c in FeSe x Te − x with x = 0 . Q = ( ,
0) and an energy of6.5 meV. We have confirmed the presence of a reso-nance in our x = 0 . Q dependence of the magnetic response in thevicinity of the resonance. In the superconducting phase( T = 1 . << T c ), transverse scans along (0 . , k ) [scanA in Fig. 1(d)] exhibit pairs of peaks at finite | k | thatdisperse with energy above 5 meV, as shown in Fig. 3(a).The color-coded map of intensity vs. Q at the resonanceenergy of 6.5 meV, Fig. 3(b), demonstrates an intrigu-ing anisotropy: the transverse peaks are not reproducedalong the longitudinal (0 . h,
0) direction as one wouldexpect from Fermi surface nesting between a pocket at Γand the four pockets about X.In the normal state ( T = 20 K), the spectral weightof the resonance is moved to lower energies, and thepeaks appear to remain split down to 4 meV [blue sym-bols in Fig. 3(a)]; the asymmetry between transverseand longitudinal directions remains the same as below T c . The dispersion of the peaks along the transverse di-rection is plotted in Fig. 3(c), with points at 10 meVand above from Lumsden et al. (For similar recent re-sults, see Refs. 25,26.) The line through the points isa fit to (cid:126) ω = E sin( π ( k − k )) with E = 121 meV for k < k = − .
09. If these excitations were like spin waves,as in CaFe As , we would expect to see cone-shapeddispersions coming out of (0 . , ± k ), which is clearly notthe case. The dispersion of isolated intensity peaks alonga single direction is quite unusual and requires considera-tion of factors beyond the degree of electronic correlation.We propose that the solution to this puzzle involvesthe coupling of spin and orbital correlations. As previ-ously mentioned, such a coupling has already been pro- FIG. 3: (color online). Momentum dependence of the spinresonance and low energy spin fluctuations. (a) Inelastic neu-tron scattering intensity as a function of Q , obtained withconstant energies, 8 meV, 6.5 meV, 5 meV, and 4 meV, at 1.5K ( < T c ) (open red circles) and 20 K ( > T c ) (filled blue cir-cles), taken along the transverse (0 . , k ) direction. The linesare fits to Gaussians; diamonds (open, 1.5 K; filled, 20 K) indi-cate fitted peak positions. Horizontal bars represent the full-width-of-the-half-maximum of the instrumental Q -resolution.(b) Color contour map summarizing 1.5-K data obtained froma series of (0 . , k ) scans centered at positions marked by redsquares. (c) Dispersion of the spin fluctuations. Open greensquares extending to high energies are taken from Ref. 24,while open red diamonds (1.5 K) and filled blue diamonds(20 K0 at low energies are our data taken from (a); hori-zontal bars are fitted peak widths at the lowest energies and T = 20 K. The line is explained in the text. posed for the antiferromagnetic phase. In fact, it hasbeen shown that the reduction of lattice symmetry canbe associated with long-range orbital ordering, and theresulting anisotropy of the superexchange parameters isconsistent with the observed spin-wave dispersions. In the present case, the orbital degeneracy of d xz and d yz orbitals re-activates the orbital freedom in the ab-sence of long-range orbital order. This changes entirelythe nature of the low-energy spin excitations.Spin correlations characterized by Q ≈ ( , d yz orbital andits ferro-orbital correlation. [Similarly, spin correlationsat Q ≈ (0 , ) are tied to the d xz orbital.] We proposethat the spin-flip excitations in the present case are con-strained by a strong coupling to orbital correlations, withtwo leading contributions illustrated in Fig. 4. First, ifwe consider flipping a single spin, we find that the or-bital also needs to flip from d yz to d xz [ c.f. Fig. 4(a)], inorder to better utilize the superexchange energy. (If theorbital remains unchanged, a local spin flip would haveclosed almost all the superexchange paths within the d yz (0,0) (0,0) (a) (b)(c) (d) ( ! , ! )( ! ,- ! ) FIG. 4: (color online). (a) Cartoon of spin+orbital flip excita-tion discussed in text, assuming finite range spin and orbitalcorrelations. Vertical (horizontal) line denotes d yz ( d xz ) or-bital. (b) Form factor for the excitation in (a). Color map:low–medium–high = blue–green–red (dark–light–gray). (c)Cartoon of inter-site spin-flip excitation. (d) Form factor mapfor the excitation in (c). and d xz subspace.) This “inter-orbital spin/orbital flip”process introduces a strongly anisotropic form factor thatgoes to zero along the longitudinal direction, as shown inFig. 4(b). This is consistent with the strong anisotropyof our neutron data and the previous observation at highenergies. Another relevant process, one associated withitinerancy, is the “inter-site spin flip” process shown inFig. 4(c); the latter has a large form factor around ( , c.f. Fig. 4(d)]. Interestingly, due to the columnar AF ar-rangement of the short-range spin correlations togetherwith the Pauli exclusion principle, our proposed inter-site spin-flip process can only propagate along the y - direction at low-energy, in good agreement with the ob-served anomalous dispersion. A quantitative analysis ofthe dispersion (beyond the scope of this paper), will re-quire evaluating the excitation energy as a function ofwave vector, taking into account both processes. In anycase, the essence of our proposal is that the spin excita-tions are hybrids of the magnons and orbitons that havebeen postulated previously. In conclusion, we have presented experimental evi-dence that the electronic and magnetic excitations ofsuperconducting FeSe . Te . are different from those ofcommon band-structure and spin-wave models. We haveproposed that the intensity anisotropy of the magneticexcitations may be explained by considering coupled spinand orbital excitations. If correct, this would imply thatnematic excitations are a key feature of the normal statefrom which the superconductivity develops. While thedetails of the magnetism are quite different, the nematiccorrelations would provide an intriguing connection tothe physics of cuprate superconductors. We are grateful to S. A. Kivelson for helpful com-ments and to A. V. Fedorov for experimental assistance.Work at the University of Virginia was supported bythe Office of Science, US Department of Energy (DOE)through DE-FG02-07ER46384. Work at Brookhaven issupported by the US DOE under Contract No. DE-AC02-98CH10886. PDJ and JMT are supported in part by theCenter for Emergent Superconductivity, an Energy Fron-tier Research Center funded by the US DOE, Office ofBasic Energy Sciences. SPINS at NCNR is supported bythe National Science Foundation under Agreement No.DMR-0454672. ALS is operated by the US DOE underContract No. DE-AC03-76SF00098 H. Hosono, Physica C , 314 (2009). K. Ishida, Y. Nakai, and H. Hosono, J. Phys. Soc. Jpn. ,062001 (2009). I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du,Phys. Rev. Lett. , 057003 (2008). K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kon-tani, and H. Aoki, Phys. Rev. Lett. , 087004 (2008). F. Kruger, S. Kumar, J. Zaanen, and J. van den Brink,Phys. Rev. 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