Figure 1

(a) Schematic in-plane spin structure of the nonsuperconducting FeTe, where the solid and hollow arrows represent two sublattices of spins which can be either parallel or antiparallel [6]. Upon substitution of Se for Te to form ${\mathrm{FeSe}}_x{\mathrm{Te}}_{1-x}$, the static long-range AF order is suppressed, and the system display strong spin excitations at incommensurate positions near $Q=(0.5,0.5)$ as shown in (b). The incommensurate scattering only appear at positions ($0.5-\delta$, $0.5+\delta$) and ($0.5+\delta$, $0.5-\delta$). Our transverse scans are along the scan direction $\mathbf{a}$, and the scan along the incommensurate position that is perpendicular to scan-$\mathbf{a}$ is marked as scan-$\mathbf{b}$. (c),(d) Schematic diagram of Fermi surfaces near $\Gamma$ and $M$ points from results of recent photoemission experiments [33, 34]. (e) In a multiband itinerant picture, quasiparticle excitations from the $\alpha 2$ band to the $\beta$ band can give rise to the upper branch of the hourglass dispersion as shown in the solid red lines. The lower branch of the dispersion is then a consequence of the excitations from the $\alpha 3$ band to the $\beta$ band. (f) Experimental determination of the spin excitation dispersions in the normal (open red circles) and SC (black filled squares) states of ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$. A full spin gap opens below $E\approx 1\mathrm{meV}$ at 1.5 K. The magnitude of $E_g$ marks the energy below which intensity of spin excitations decrease below $T_c$, whereas $E_r$ indicates the resonance energy. The dispersion curves are obtained by fitting two Gaussians on linear backgrounds through transverse scans in Figs. 2, 3. We note that the incommensurability at 2 meV at 20 K is obtained by fitting the difference between the 20 K data and 1.5 K data. The horizontal error bars are the fitted errors of the incommensurability. (g) Hourglass dispersion in the NSC ${\mathrm{FeSe}}_{0.45}{\mathrm{Te}}_{0.55}$ at 4 and 15 K.Reuse & Permissions

Figure 2

(a) Constant-energy scans at $E=1\mathrm{meV}$ along the scan-$\mathbf{a}$ direction below (solid squares) and above $T_c$ (open circles). The normal-state incommensurate scattering is completely suppressed below $T_c$. The solid line is a fit of the data using two Gaussians on a sloped linear background. The data at 1.5 K are featureless indicating the presence of a full spin gap at this energy. (b) Constant-energy scans along the scan-$\mathbf{b}$ direction below and above $T_c$. The data confirm that the normal-state magnetic scattering is incommensurate and centered at ($0.5-\delta$, $0.5+\delta$) and ($0.5+\delta$, $0.5-\delta$) with $\delta =0.132\pm 0.007$ at $E=1\mathrm{meV}$. The scattering again become featureless below $T_c$. (c) The temperature dependence of the scattering at $Q=(0.37,0.63)$ and $E=1\mathrm{meV}$ (left scale) decreases below $T_c$, while the scattering at the resonance energy [$Q=(0.5,0.5)$ and $E=6\mathrm{meV}$] increases below $T_c$ (right scale). (d) Similar scans as (a) in the $x=0.45$ NSC sample.Reuse & Permissions

Figure 3

Constant-energy scans along the scan-$\mathbf{a}$ direction above and below $T_c$ for energies (a) 2 meV; Here the transverse scans have three peaks in the normal state, centered at ($0.5-\delta$, $0.5+\delta$), (0.5,0.5), and ($0.5+\delta$, $0.5-\delta$), and these peaks are suppressed but not eliminated below $T_c$. (b) 3, (c) 4.5, (d) 6; (e) 7.5, and (f) 9.5 meV. The solid lines are Gaussian fits to the data on linear sloped backgrounds. Superconductivity has opposite effect on spin excitations below and above $E=4.5\mathrm{meV}$.Reuse & Permissions

Figure 4

Constant-$Q$ scans at $Q=(0.5,0.5)$ for temperatures above and below $T_c$ in (a) $x=0.4$ and (b) $x=0.45$ samples. (c) Transverse scan at 6 meV in the $x=0.45$ sample that shows weak temperature dependence. (d) Magnetic excitation at 3 meV centered at (0.5,0,0) in the $x=0.45$ sample.Reuse & Permissions