The origin of the superconducting state in the recently discovered Fe-based materials1,2,3 is the subject of intense scrutiny. Neutron scattering4,5,6,7 and NMR (ref. 8) measurements have already demonstrated a strong correlation between magnetism and superconductivity. A central unanswered question concerns the nature of the normal-state spin fluctuations that may be responsible for the pairing. Here we present inelastic neutron scattering measurements from large single crystals of superconducting and non-superconducting Fe1+yTe1−xSex. These measurements indicate a spin fluctuation spectrum dominated by two-dimensional incommensurate excitations extending to energies greater than 250 meV. Most importantly, the spin excitations in Fe1+yTe1−xSex have four-fold symmetry about the (1, 0) wavevector (square-lattice (π,π) point). Moreover, the excitations are described by the identical wavevector and can be characterized by the same model as the normal-state spin excitations in the high-TC cuprates9,10,11. These results demonstrate commonality between the magnetism in these classes of materials, which perhaps extends to a common origin for superconductivity.
The discovery of superconductivity in LaFeAsO1−xFx with TC=28 K (ref. 1) sparked a flurry of scientific activity and TC rapidly increased to ∼55 K on replacing La with other rare-earth elements2,12,13. In addition to the RFeAsO family of compounds, superconductivity was also discovered in AFe2As2 (ref. 3), LiFeAs (ref. 14), and in the alpha phase of Fe1+yTe1−xSex (refs 15, 16). These materials share common structural square layers with Fe coordinated with either a pnictogen or a chalcogen. The unit cell contains two Fe atoms generating a reciprocal space rotated by 45∘ from the conventional square lattice (see Fig. 1a). In RFeAsO and AFe2As2, the parent compounds show long-range spin-density-wave order characterized by the wavevector Q=(1/2,1/2,L) (refs 17, 18, 19). Doping suppresses magnetic order, allowing superconductivity to emerge with the concomitant appearance of a resonance in the spin fluctuation spectrum4,5,6,7. However, the resonance probably contains only a small fraction of the total magnetic spectral weight and, consequently, understanding the role magnetism has in the superconductivity requires a detailed understanding of the higher energy spectrum of magnetic excitations.
The Fe1+yTe1−xSex materials are ideal candidates for a study of the magnetic excitations as large single crystals, necessary for detailed inelastic neutron scattering studies, may be grown. However, these materials differ from other Fe-based superconductors in that the Fe1+yTe endpoint member (for small y) orders magnetically with a structure described by the wavevector (1/2, 0, 1/2) (ref. 20) as opposed to (1/2, 1/2, L). Despite this difference, superconducting samples of Fe1+yTe1−xSex with higher Se content show a magnetic resonance at the same (1/2, 1/2) wavevector as other Fe-based superconductors7,21 suggesting commonality in the magnetic response. To explore the magnetic excitations, inelastic neutron scattering measurements were carried out using the MERLIN spectrometer at the ISIS neutron scattering facility and the ARCS spectrometer at the Spallation Neutron Source. Measurements of lower energy excitations were carried out using the HB1 and HB3 triple-axis spectrometers at the High Flux Isotope Reactor. The single-crystal samples of Fe1.04Te0.73Se0.27 and FeTe0.51Se0.49 studied here were prepared as in ref. 22. Bulk measurements indicate weak, probably filamentary, superconductivity in Fe1.04Te0.73Se0.27 and bulk superconductivity in FeTe0.51Se0.49. Neither sample shows long-range magnetic order; however, for x=0.27, short-range magnetic order is observed20.
Figure 2a–h summarizes the measured magnetic excitations at several energy transfers for both the x=0.27 and x=0.49 samples. We first note that the observed spectrum of magnetic excitations is two-dimensional (2D) in nature. Measurements at multiple sample-rotation angles were combined to allow for examination of the L dependence at fixed (H,K) coordinates. Such measurements indicate intensity that varies only weakly with L (see Supplementary Information), as expected for 2D excitations. This is consistent with recent measurements of a 2D magnetic resonance in FeSe0.4Te0.6 (ref. 21).
The low-energy magnetic response (Fig. 2a,b) for the x=0.27 sample is characterized by two peaks at wavevectors near (1/2, 1/2). Interestingly, the data do not show four-fold symmetry around this wavevector as expected for the nuclear cell of the P4/n m m space group, but rather form a quartet around the (1, 0) wavevector. With increasing energy, the peaks disperse away from (1/2, 1/2) towards (1, 0) as shown schematically in Fig. 1b. At higher energies, the excitations continue to disperse towards (1, 0) but evolve from spots into rings (Fig. 2c) centred on this wavevector. Eventually, as shown for an energy transfer of 120 meV in Fig. 2d, the excitations evolve into broad spots centred at (1, 0). For the superconducting x=0.49 sample, the low-energy spectrum appears as a series of asymmetric spots (Fig. 2e). However, data measured at a higher energy transfer of 22 meV (Fig. 2f) show separated peaks similar to those in the x=0.27 sample. This can easily be understood by considering that the displacement of these peaks away from (1, 0) is larger in the x=0.49 sample such that the pair of peaks around (1/2, 1/2) have moved closer together and overlap significantly. At an energy of 45 meV (Fig. 2g), the characteristic wavevector appears similar in the two samples but the x=0.49 scattering appears to have not fully evolved into the rings of scattering present in the x=0.27 sample (Fig. 2c). At high energies, the scattering is similar in the two samples, as can be seen by comparing Fig. 2d and h. The excitations persist to energy transfers greater than 250 meV (see Supplementary Information) with Q-dependence similar to that shown at 120 meV for all higher energies.
Examination of the wavevector describing these excitations reveals similarities with the high-TC cuprates. The quartet of peaks is characterized by wavevectors (1±ξ,±ξ) and that, in square-lattice notation, corresponds to (π±ξ,π) and (π,π±ξ) as shown in Fig. 1b. This is precisely the same wavevector as the low-energy excitations observed in La2−xSrxCuO4 (ref. 9) and YBa2Cu3O6+x (refs 10, 11), indicating remarkable commonality in the excitation spectrum of these two classes of high-TC superconductors. Furthermore, the evolution of the scattering from well-defined peaks at low energies to broadened rings at higher energies is a characteristic property of magnetic excitations in the cuprates23,24. The magnitude of ξ, however, is much larger in Fe1+yTe1−xSex, resulting in low-energy excitations displaced away from (1, 0) and much closer to (1/2, 1/2).
At low energies, the largest difference between the two concentrations becomes evident as shown in Fig. 3a,b. In addition to the excitations near (1/2, 1/2), an extra component centred near (1/2, 0) is present in the x=0.27 sample (also visible in Fig. 2a). With decreasing energy, the intensity of this component increases, eventually forming the short-range order observed previously for samples with a similar concentration20,25. It has been suggested26 that excess Fe in Te-rich samples results in local moments that may provide a pair-breaking mechanism destroying superconductivity. The component of scattering observed near (1/2, 0) is absent in the x=0.49 sample with no excess Fe (Fig. 3b). Furthermore, the scattering near (1/2, 0) exists inelastically for all energies below ∼10 meV and, as such, exists well below the superconducting gap, potentially providing a pair-breaking mechanism. These observations are consistent with the extra component near (1/2, 0) existing as a result of the influence of extra Fe in the x=0.27 sample.
To quantify the dispersion of the spin excitations, the data were fitted using the phenomenological Sato–Maki function27 previously used for the cuprates24
The form for R(Q) in equation (2) describes excitations four-fold symmetric about (HC,KC)=(1,0). As discussed below, δ parameterizes the dispersion, λ defines the evolution of the spectrum from peaks (large λ) to rings (small λ) and κ is a broadening parameter.
The results of fits to the data presented in Fig. 2a–h using the Sato–Maki function convolved with instrumental resolution are shown in Fig. 2i–l (m–p) for x=0.27 (0.49). The fits agree well with the measurements over the full range of measured energies. The fit quality is also demonstrated in Fig. 4d–g for cuts along , indicating excellent agreement over a wide range of wavevector and energy transfer. A spin excitation spectrum accurately described by the identical model in both Fe1+yTe1−xSex and the cuprates is further evidence of commonality in these two classes of superconductor. The same Sato–Maki function can be used to describe the extra component in the x=0.27 sample near (1/2, 0) with a rotated R(Q) factor (see Supplementary Information) and the fits shown in Figs 3c and 2i contain both components, again yielding excellent agreement with the data.
The best fit value of δ parameterizes the dispersion. If we define the characteristic wavevector as , then . The resulting dispersion (Fig. 4a) demonstrates excitations dispersing from a wavevector near (1/2, 1/2) (ξ=−0.5) towards (1, 0) (ξ=0). The shape of the dispersion is reminiscent of the ‘hour glass’ dispersion observed in the cuprates24,28. However, unlike the cuprates, the high-energy excitations of Fe1+yTe1−xSex remain centred near (1, 0) with no evidence for dispersion away from this wavevector. It is important to note that, for both concentrations, the dispersion does not approach the commensurate (1/2, 1/2) wavevector on approaching the elastic condition and, therefore, both samples show an incommensurate excitation spectrum. For energies greater than ∼50 meV, the dispersions are consistent for the two concentrations. However, for lower energies, |ξ| is larger for x=0.49, indicating excitations displaced closer to the (1/2, 1/2) wavevector with larger Se content. This can also be clearly seen in comparing the cuts in Fig. 4b with 4d (25 meV) and 4c with 4e (70 meV). The peaks in the 25 meV data are at clearly different wavevectors, but the distribution of scattering intensity is nearly identical at 70 meV for the two concentrations. It is interesting to note that the sample (x=0.49) with normal-state excitations closer to the resonance wavevector shows bulk superconductivity, whereas only weak superconductivity is observed in the sample with normal-state excitations displaced further from this wavevector.
Finally, we discuss the implications of the observed Q-dependence of the magnetic excitations. As a consequence of the coordination of the chalcogen atoms, the real-space P4/n m m unit cell contains two Fe atoms. On the other hand, as the system is not magnetically ordered, if one considers magnetism primarily associated with the Fe atoms, the effective magnetic unit cell is described by a 2D square lattice. The Brillouin zone of each of these lattices is illustrated in Fig. 1a. As seen in Fig. 2, the observed magnetic scattering shows periodicity compatible with the Fe sublattice Brillouin zone. This is consistent with the periodicity of spin fluctuations observed in the high-TC cuprates, as expected because cuprate magnetism is dominated by Cu atoms that also form a square lattice. The essential magnetism in both Fe1+yTe1−xSex and the cuprates can be captured by the identical model even though the crystal structures themselves have different symmetries. We note that caution is necessary in comparing the Q-dependence of experimental data with theoretical calculations. Some published calculations have been presented in a 2D Brillouin zone based on the P4/n m m lattice. This Brillouin zone is smaller than the square-lattice Brillouin zone and, presented in this manner, calculations fold excitations in the zone centred at (1, 0) back to the zone centred at (0, 0) (ref. 29). This superposes the magnetic response in these two zones, making it difficult to extract the true Q-dependence as measured experimentally. Calculations carried out in the square-lattice Brillouin zone should result in the symmetry of the measured excitation spectrum as confirmed by calculations of the Q-dependent spin susceptibility and gap functions30.
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We acknowledge discussions with D. Singh and T. Maier. This work was supported by the Scientific User Facilities Division and the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy.
The authors declare no competing financial interests.
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Lumsden, M., Christianson, A., Goremychkin, E. et al. Evolution of spin excitations into the superconducting state in FeTe1−xSex. Nature Phys 6, 182–186 (2010). https://doi.org/10.1038/nphys1512
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