# Normal-state hourglass dispersion in spin excitations of FeSe x Te$_{1}$$_{−}$ x 

Shiliang Li, 1 Chenglin Zhang, 2 Meng Wang, 1, 2 Hui-qian Luo, 1 Xingye Lu, 1 Enrico Faulhaber, 3, 4 

Astrid Schneidewind, 3, 4 Peter Link, 4 Jiangping Hu, 5, 1 Tao Xiang, 1, 6 and Pengcheng Dai 2, 7, 1,$_{∗}$ 

$^{1}$Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China † 

2 Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA 3 

Gemeinsame Forschergruppe HZB - TU Dresden, D-14109 Berlin, Germany 

4 Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM-II), TU M ¨ u nchen, D-85747 Garching, Germany 5 

Department of Physics, Purdue University, West Lafayette, IN 47907, USA 

$^{6}$Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China 

7 Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA 

We use cold neutron spectroscopy to study the low-energy spin excitations of superconduct- ing (SC) FeSe 0 . 4 Te 0 . 6 and essentially non-superconducting (NSC) FeSe 0 . 45 Te 0 . 55 . In contrast to BaFe 2 − x (Co,Ni) x As 2 , where the low-energy spin excitations are commensurate both in the SC and normal state, the normal-state spin excitations in SC FeSe 0 . 4 Te 0 . 6 are incommensurate and show an hourglass dispersion near the resonance energy. Since similar hourglass dispersion is also found in the NSC FeSe 0 . 45 Te 0 . 55 , we argue that the observed incommensurate spin excitations in FeSe 1 − x Te x are not directly associated with superconductivity. Instead, the results can be understood within a picture of Fermi surface nesting assuming extremely low Fermi velocities and spin-orbital coupling. 

The discovery of antiferromagnetism in the Fe-based high-transition (high- T$_{c}$ ) temperature superconductors [1–6] has reinvigorated research in understanding the role of magnetism in the superconductivity [7–10]. Among the different classes of iron pnctides, FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ has the simplest crystal structure, composed of layers of Fe atoms forming a square lattice with Se/Te atoms centered above or below these squares alternating in a checker- board fashion (Fig. 1a) [3–6]. To obtain a comprehen- sive understanding for the role of magnetism in the su- perconductivity of FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ , it is important to de- termine the energy ( E ) and momentum ( Q ) dependence of its spin excitations in the normal and superconduct- ing (SC) state, and compare the results with that of the other Fe-based [11–16] and cuprate high- T$_{c}$ super- conductors [17, 18]. For cuprates such as La$_{2}$$_{−}$$_{x}$Sr$_{x}$CuO$_{4}$ [17] and YBa$_{2}$Cu$_{3}$O$_{6+}$$_{x}$ [18], the low-energy spin exci- tations consist of a spin gap, a quartet of incommensu- rate peaks merging into a collective excitation called the resonance, and then dispersing outward again at ener- gies above the mode forming a hourglass-like dispersion. If the resonance in cuprates arises from metallic nested Fermi surfaces, the incommensurate scattering below the resonance signal the strong anisotropy of the d -wave SC gap [19, 20]. In contrast, the experimental observation of a commensurate resonance above a clean spin gap for the Fe-based BaFe$_{2}$$_{−}$$_{x}$(Co,Ni)$_{x}$As$_{2}$ superconductors [12–16] has been taken as evidence that the mode here arises from quasiparticle excitations from sign reversed isotropic s -wave SC gaps on the hole and electron Fermi pockets (Figs. 1c-1e) [7, 21, 22]. If Fermi surfaces in FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ are similar to that of BaFe$_{2}$$_{−}$$_{x}$(Co,Ni)$_{x}$As$_{2}$ [23], one should expect low energy spin excitations to 

PACS numbers: 74.70.Dd, 75.25.+z, 75.30.Fv, 75.50.Ee 

behave similarly as well. Indeed, the observation of a commensurate neutron spin resonance in FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ at x = 0 . 4 , 0 . 5 [24, 25] appears to confirm this conclusion. Although recent neutron scattering measurements have found incommensurate peaks (Fig. 1b) at energies near and above the resonance energy [26–29], these results are consistent with the current theory [27] and incommen- surability has been interpreted as the signature of spin- orbital correlations [28]. If the SC gaps in FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ for x ∼ 0 . 5 are indeed isotropic s -wave, the resonance should not show an hourglass-like dispersion as in the case of cuprates [27]. 

Surprisingly, we found that spin excitations in SC FeSe$_{0}$$_{.}$$_{4}$Te$_{0}$$_{.}$$_{6}$ have an hourglass-like dispersion (Fig. 1f) in the normal state. On cooling below T$_{c}$ , the excita- tion spectrum opens a small spin gap before merging into the resonance. In the nearly non-superconducting (NSC) FeSe$_{0}$$_{.}$$_{45}$Te$_{0}$$_{.}$$_{55}$ that shows weak resonance and no spin gap, similar hourglass dispersion was also found. There- fore, such dispersion must be unrelated to the SC elec- tronic gap, which is contrary to the case of cuprate su- perconductors [17–20]. Instead, we argue that the results are similar to that for pure chromium [30, 31] and can be understood by the multi-band nature of the system. 

We have carried out our inelastic neutron scattering experiments using the PANDA cold triple-axis spectrom- eter at the FRM-II, TU M¨ unchen, Germany. We used pyrolytic graphite PG(0 , 0 , 2) as monochromator and an- alyzer without any collimator. The final neutron wave vector was fixed at k$_{f}$ = 1 . 55 ˚ A $_{−}$1 with a cooled Be filter before the analyzer. The energy resolution is about 0.15 meV. We chose to study SC FeSe$_{x}$Te$_{1}$$_{−}$$_{x}$ with x = 0 . 4 because previous measurements on similar samples have 

