Coexistence of superconductivity and short-range double-stripe spin correlations in Te-vapor annealed ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ ($x\le 0.2$)

In as-grown bulk crystals of ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ with $x\lesssim 0.3$, excess Fe ($y>0$) is inevitable and correlates with a suppression of superconductivity. At the same time, there remains the question as to whether the character of the antiferromagnetic correlations associated with the enhanced anion height above the Fe planes in Te-rich samples is compatible with superconductivity. To test this, we have annealed as-grown crystals with $x=0.1$ and 0.2 in Te vapor, effectively reducing the excess Fe and inducing bulk superconductivity. Inelastic neutron scattering measurements reveal low-energy magnetic excitations consistent with short-range correlations of the double-stripe type; nevertheless, cooling into the superconducting state results in a spin gap and a spin resonance, with the extra signal in the resonance being short range with a mixed single-stripe/double-stripe character, which is different than other iron-based superconductors. The mixed magnetic character of these superconducting samples does not appear to be trivially explainable by inhomogeneity.

Figure 1

Phase diagram of ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ as a function of Se content ($x$) and temperature ($T$). The red circles represent the Néel temperature ($T_N$); blue circles represent the as-grown samples' superconducting onset temperature $T_c$; purple circles represent the superconducting onset temperature in the treated samples. Data from Refs. [38, 42] are included here.

Figure 2

(a) Zero-field-cooled magnetization measurements by SQUID with a 10 Oe field perpendicular to the $a\text{−}b$ plane for all samples: $x=0.1$ (green solid line) and $x=0.2$ (purple solid line). For SI unit, $1\mathrm{emu}/(\mathrm{g}\mathrm{Oe})=4\pi {10}^{-3}{\mathrm{m}}^3$/kg. (b) Diagram of reciprocal space indicating the characteristic wave vectors ${\mathbf{Q}}_{\mathrm{SAF}}$ and ${\mathbf{Q}}_{\mathrm{DSAF}}$. (c) Elastic neutron-scattering measurements performed on $x=0.1$ sample around magnetic order peak at (0.5,0,0.5) measured on BT-7. Intensity profiles along [100] direction ($H$ scans) at temperatures below ($T=3$ K, red) and above $T_N$ (50 K, blue). The horizontal (black) bar represents the $H$ resolution. (d) The integrated magnetic peak intensity (from fitted Gaussian peak intensity) vs temperature. The error bars represent the square root of the number of counts.

Figure 3

Contour intensity maps of magnetic neutron scattering intensity measured on HB-1 in $\left(HK0\right)$ plane at energy transfer $\hslash \omega =6.5$ meV. The maps are plotted for the $x=0.1$ (left column) and $x=0.2$ (right column) samples at sample temperatures: (a) and (b) 5 K, (c) and (d) 20 K, and (e) and (f) 100 K. The data have been folded from the first quadrant ($H>0$, $K>0$). Intensity scale is the same in all panels and the data have been smoothed.

Figure 4

Contour intensity maps of temperature difference of magnetic neutron scattering intensity measured on HB-1 in $\left(HK0\right)$ plane at energy transfer $\hslash \omega =6.5$ meV. The maps are plotted for the $x=0.1$ (left column) and $x=0.2$ (right column) samples at temperature differences of: (a) and (b) $I$(100 K)-$I$(20 K) and (c) and (d) $I$(5 K)-$I$(20 K). The data have been folded from first quadrant ($H>0$, $K>0$). (e) Intensity calculated based on the same UDUD spin-plaquette model described in Refs. [32, 45], with the volume ratio of interplaquette correlation being 25% SAF and 75% DSAF. Intensity scale is the same in all panels and the data have been smoothed.

Figure 5

Contour intensity maps of magnetic neutron scattering intensity in energy-momentum space along the transverse direction. The maps are plotted for the $x=0.1$ (left column, measured on BT-7) and $x=0.2$ (right column, measured on HB-1) samples at sample temperatures: (a) and (b) 5 K and (c) and (d) 20 K. The data have been smoothed.

Figure 6

Constant energy scans of magnetic scattering intensity along the transverse direction at excitation energy 6.5 meV for the (a) $x=0.1$ and (b) $x=0.2$ samples at sample temperatures: 3 K (red circles) and 20 K (blue circles). The wave vector dependence of the spin resonance from the temperature difference $I$(3 K)-$I$(20 K) is plotted in (c) $x=0.1$ and (d) $x=0.2$. The purple lines are model calculation based on the same UDUD spin plaquette model described in Refs. [32, 45], with the volume ratio of interplaquette correlation being 25% SAF and 75% DSAF in (c) and 20% SAF and 80% DSAF in (d). The green dashed lines are a similar model calculation based on 100% SAF correlations. (e) and (f) The temperature dependence of the spin resonance from peak intensities at $(0.6,0.4,0)$ at 6.5 meV for respective samples. The error bars in (a), (b), (e), and (f) represent the square root of the number of counts and error bars in (c) and (d) are derived from the square root of the number of counts.