Thermal evolution of antiferromagnetic correlations and tetrahedral bond angles in superconducting ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$

It has recently been demonstrated that dynamical magnetic correlations measured by neutron scattering in iron chalcogenides can be described with models of short-range correlations characterized by particular choices of four-spin plaquettes, where the appropriate choice changes as the parent material is doped towards superconductivity. Here we apply such models to describe measured maps of magnetic scattering as a function of two-dimensional wave vectors obtained for optimally superconducting crystals of ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$. We show that the characteristic antiferromagnetic wave vector evolves from that of the bicollinear structure found in underdoped chalcogenides (at high temperature) to that associated with the stripe structure of antiferromagnetic iron arsenides (at low temperature); these can both be described with the same local plaquette, but with different interplaquette correlations. While the magnitude of the low-energy magnetic spectral weight is substantial at all temperatures, it actually weakens somewhat at low temperature, where the charge carriers become more itinerant. The observed change in spin correlations is correlated with the dramatic drop in the electronic scattering rate and the growth of the bulk nematic response upon cooling. Finally, we also present powder neutron diffraction results for lattice parameters in ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ indicating that the tetrahedral bond angle tends to increase towards the ideal value upon cooling, in agreement with the increased screening of the crystal field by more itinerant electrons and the correspondingly smaller splitting of the Fe $3d$ orbitals.

Figure 1

Comparison of the elastoresistance coefficient $m_{66}$ for $x=0.4$ (dashed line) [39], inverse scattering rate of the narrow Drude component from optical conductivity measurements of $x=0.45$ (open squares) [42], and the ratio of 7-meV magnetic spectral weight integrated about the spin-stripe wave vector $(\frac{1}{2},\frac{1}{2})$ and the double-stripe wave vector $(\frac{1}{2},0)$ (filled circles connected by solid line), taken from Fig. 6, with error bars reflecting counting statistics. All quantities have been normalized at 200 K.

Figure 2

(a) The two-Fe unit cell used in the paper. The circles denote Fe atom positions. The red and blue arrows respectively denote the $[1,0]$ and $[1,1]$ directions in real space. (b) $Q_{AF}=(0.5,0.5)$, location of the spin resonance in the $(H,K,0)$ plane. The dashed arrow denotes the transverse direction, along which we plot the inelastic magnetic neutron scattering for temperatures of (c) 6 K, (d) 20 K, and (e) 80 K, measured from the SC50 sample on SEQUOIA.

Figure 3

Inelastic magnetic neutron scattering from the SC70 sample measured on HYSPEC at energy transfers $\hslash \omega =13$ meV (a), (b), (c); 10 meV (d), (e), (f); and 7 meV (g), (h), (i). The sample temperatures are 8 K (a), (d), (g); 100 K (b), (e), (h); and 300 K (c), (f), (i). All slices were taken with an energy width of 2 meV. Measurements, covering approximately two quadrants, have been symmetrized to be 4-fold symmetric, consistent with sample symmetry. Intensity scale is the same in all panels, but 13-meV data have been multiplied by 1.5 to improve visibility. Black regions at the center of each panel are outside of the detector range. Panels (j), (k), (l) are model calculations simulating the 7-meV data, as described in the text, based on weakly correlated slanted UDUD spin plaquettes [see Figs. 5 and 5]. The wave vectors for the AFM interplaquette correlations used in the calculation are (j) 100% $Q_{\mathrm{SAF}}$, (k) 50% $Q_{\mathrm{SAF}}$ and 50% $Q_{\mathrm{DSAF}}$, and (l) 100% $Q_{\mathrm{DSAF}}$.

Figure 4

Inelastic magnetic neutron scattering measured at energy transfers $\hslash \omega =13$ meV (top row), 10 meV (second row from the top), and 7 meV (third row from the top) on HYSPEC. All slices were taken with an energy width of 2 meV. The sample used is the NSC45 sample. The temperatures for the measurements are 8 K, 100 K, 300 K, from left to right, respectively.

Figure 5

Schematics of the spin plaquettes in the weakly correlated spin-liquid model described in the text. (a) A canted UDUD plaquette with modulation wave vector ${\mathbf{Q}}_{\mathrm{SAF}}$. (b) Canted UDUD plaquette with ${\mathbf{Q}}_{\mathrm{DSAF}}$. (c) Square UDUD plaquette with ${\mathbf{Q}}_{\mathrm{SAF}}$. (d) Square UDUD plaquette with block antiferromagnetic correlations. (e) Square UUUU plaquette with block antiferromagnetic correlations. The frames (f) to (j) are model simulations described in the text, based on the liquid-like spin plaquette models in (a) to (e), respectively.

Figure 6

Inelastic neutron scattering intensity measured at $\hslash \omega =7$ meV with energy width $\delta E=1$ meV from the SC70 sample on HYSPEC. (a) Raw intensity measured at ${\mathbf{Q}}_{\mathrm{DSAF}}=(0.5,0)$ (blue diamonds) and ${\mathbf{Q}}_{\mathrm{SAF}}=(0.5,0.5)$ (red circles). The numbers shown in the plot are averaged intensities taken within a square region with $\delta H=0.1$ and $\delta K=0.1$ (r.l.u.) centered at the measurement wave vectors. The background is measured by averaging intensities around $(1,0)$ and $(1,1)$, shown as black squares. (b) Background-subtracted intensities at ${\mathbf{Q}}_{\mathrm{DSAF}}$ (blue diamonds) and ${\mathbf{Q}}_{\mathrm{SAF}}$ (red circles). The solid line is the calculated detailed-balance factor. (c) Integrated intensity over the full Brillouin zone centered at (0,0).

Figure 7

Lattice parameters $a$ (a), and $c$ (b), for ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ as a function of $x$, measured by neutron powder diffraction at 300 K on NOMAD. Statistical uncertainties for $a$ and $c$ are smaller than the symbol size. The dashed lines simply connect the points at $x=0$ and 1.

Figure 8

(a) Change in $a$ and $c$ lattice parameters, normalized to 300 K, as a function of temperature for the $x=0.50$ sample. Statistical uncertainties are comparable to the symbol size. (b) Change in $a/c$, normalized to 300 K, as a function temperature for ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$; the values of $x$ are noted in the symbol legend. The average of in-plane lattice parameters was used for $a$ in the low-temperature phase of $x=0$.