Temperature dependence of the resonance and low-energy spin excitations in superconducting FeTe${}_{0.6}$Se${}_{0.4}$

We use inelastic neutron scattering to study the temperature dependence of the low-energy spin excitations in single crystals of superconducting FeTe${}_{0.6}$Se${}_{0.4}$ ($T_c=14$ K). In the low-temperature superconducting state, the imaginary part of the dynamic susceptibility at the electron and hole Fermi-surfaces nesting wave vector $Q=(0.5,0.5)$, ${\chi }^{\prime \prime }(Q,\omega )$, has a small spin gap, a two-dimensional neutron spin resonance above the spin gap, and increases linearly with increasing $\hslash \omega$ for energies above the resonance. While the intensity of the resonance decreases like an order parameter with increasing temperature and disappears at temperature slightly above $T_c$, the energy of the mode is weakly temperature dependent and vanishes concurrently above $T_c$. This suggests that in spite of its similarities with the resonance in electron-doped superconducting BaFe${}_{2-x}$(Co,Ni)${}_x$As${}_2$, the mode in FeTe${}_{0.6}$Se${}_{0.4}$ is not directly associated with the superconducting electronic gap.

Figure 1

(a) Diagram of the Fe spin ordering with the shaded region defining the magnetic unit cell. (b) Cartoon of the scan directions though the $(1/2,1/2,L)$ nesting vector. The inset illustrates the direction in the $[H,K]$ plane to which scans were confined. Excitations at $(1/2,1/2,L)$ in FeTe${}_{1-x}$Se${}_x$ consist of two incommensurate peaks that spread away from one another in the transverse direction. The red circles in the inset depict these excitations with the radius of the circles equal to twice the FWHM of the (1/2, 1/2, 0), 7.5 meV resonance peaks measured on crystals from the same batch on a different experiment. The separation of their centers is set to agree with the dispersion mapped out in this previous experiment (Ref. 34). (c)–(e) Energy scans about the 7 meV resonance position above and below $T_c$ for $L=0,1/2,1$. Clear intensity gain is observed inside the superconducting state. The background at $L=0$ is plotted above and below $T_c$ and is found to be identical, allowing direct temperature subtraction of the scans with no need for background correction. (f) Temperature subtraction of energy scans shown in panels (c)–(e) demonstrating no observable dispersion of the resonance energy along $L$.

Figure 2

(a) Raw data for energy scans at $Q=(1/2,1/2,1/2)$ for multiple temperatures below $T_c$. At 2 K the 7 meV resonance is clearly present. A strong reduction in scattering for energies below 4 meV is also visible, indicating the opening of a gap in the system. Subsequent $Q$ scans, however, show that this is not a true gap. As the temperature increases to $T_c$ the resonance suppresses and the partial gap closes up. (b) Temperature subtraction of scans shown in panel (a). All of the data is fit with a Gaussian leaving the center energy as a free parameter to be determined. (c) Position of the resonance energy vs temperature as determined from the fits in panel (b); note that circles above $T=15$ K are meant to indicate that the resonance has been completely suppressed. The temperature dependence of the superconducting gap (Ref. 42) is also graphed, explicitly demonstrating that the resonance does not shift in energy as a function of temperature so as to remain inside $2\Delta$ as required by the spin exciton scenario.

Figure 3

(a),(b) Raw $Q$-scan data along $[H,H]$ and $L$, respectively, at $E_R=6.5$ meV at several temperatures. (c),(d) ${\chi }^{\prime \prime }(Q,\omega )$ is determined by subtraction of the background and correcting for the Bose factor. In (c) the 100 K data were used as a final background subtraction in order to remove a spurion at (0.45, 0.45, 0.5) and a phonon tail for points near (0.7, 0.7, 0.5). (d) The intensity gain due to the resonance is determined by subtraction of the 2 and 20 K data. The resulting signal is very broad and fits well to the Fe${}^{2+}$ form factor; a testament to the two-dimensional (2D) nature of the resonant mode. (e),(f) Temperature dependence of the resonance for $Q=(1/2,1/2,1/2)$ and $E=6.8$ meV. The resonance suppresses as an order parameter as $T_c$ is approached.

Figure 4

(a),(b) $Q$-scan data along the $[H,H]$ direction for $L=1$ and $E=3$ meV. The scattering becomes stronger as $T_c$ is approached from higher temperatures; upon entering the superconducting state the intensity drops significantly by 2 K but does not fully gap. (c) Temperature dependence at 3 meV inside of the pseudo-spin-gap region reveals that near $T_c$ a gap begins to form but never fully forms by base temperature. (d) $S(Q,\omega )$ of the temperature scan as determined by interpolating and subtracting the background collected using A3 rocking curves. Yellow diamonds correspond to cross checks with fitted $Q$ scans from panels (a) and (b). Since the $Q$ scans and temperature scan were collected on different experiments, the data sets were not normalized to one another by monitor count but rather shifted to coincide at 20 K.

Figure 5

(a) Raw $Q$-scan data along the $[H,H]$ direction for $L=1$ and $E=11$ meV. (b) ${\chi }^{\prime \prime }(Q,\omega )$ determined by background subtraction and correcting for the Bose factor. The resonance is no longer visible; instead the scattering at 2 K is nearly identical to 20 K. Upon entering the normal state, the intensity begins dropping monotonically with increasing temperature but remains robust up to 100 K. (c),(d) Temperature scan at (1/2, 1/2, 1/2) for $E=11$ meV. Red stars correspond to cross checks with fitted peak intensities from $Q$ scans in panel (a) that have been form factor corrected and normalized by monitor count.

Figure 6

(a) Energy scans focusing on temperatures above $T_c$. (b) The background subtraction of ${\chi }^{\prime \prime }(Q,\omega )$ is determined from $Q$ scans. Aside from the resonance in the 2 K data, all other energy scans follow a similar linear trend; fanning out as a function of temperature.