Incommensurate itinerant antiferromagnetic excitations and spin resonance in the ${\text{FeTe}}_{0.6}{\text{Se}}_{0.4}$ superconductor

We report on inelastic neutron-scattering measurements that find itinerantlike incommensurate magnetic excitations in the normal state of superconducting ${\text{FeTe}}_{0.6}{\text{Se}}_{0.4}$ $\left(T_c=14\text{K}\right)$ at wave vector ${\mathbf{Q}}_{inc}=\left(1/2\pm ϵ,1/2\mp ϵ\right)$ with $ϵ=0.09\left(1\right)$. In the superconducting state only the lower energy part of the spectrum shows significant changes by the formation of a gap and a magnetic resonance that follows the dispersion of the normal-state excitations. We use a four band model to describe the Fermi-surface topology of this iron-based superconductors with the extended $s(\pm )$ symmetry and find that it qualitatively captures the salient features of these data.

Figure 1

(Color online) Typical INS transverse scans through $\mathbf{Q}=\left(1/2,1/2\right)$ at fixed $\hslash \omega$ measured from a single crystal of ${\text{FeTe}}_{0.6}{\text{Se}}_{0.4}$ at [(a) and (b)] 2 K below $T_c$ and [(c) and (d)] at 20 K above $T_c$. The solid lines through the data are Gaussian fits to the magnetic excitations. For clarity, data and fits are shifted along the $y$ axis by an arbitrary amounts. The position of the background for each scan is indicated by a horizontal line. The black horizontal bar in panel (a) represent the expected $Q$ resolution.

Figure 2

(Color online) Color maps of the transverse fixed energy scans along $\left(1/2+ϵ,1/2-ϵ,0\right)$ for energy transfers between 2 and 12 meV measured at (a) 20 K and (b) 2 K. Black points indicate the center of Gaussian peaks fitted to the experimental data while the red lines illustrate the dispersions of these peak centers. In (b) black points represent centers of Gaussian from the subtraction shown in Fig. 3b. The dispersion of the normal state is reproduced by red lines in the superconducting state to illustrate that the higher energy excitations have not changed their position below $T_c$. RPA calculations depicting the magnetic excitations of the (c) normal and (d) superconducting state. In (c) we over plot the experimental paramagnon dispersion while in (d) we show the measured magnetic-resonance excitations as white circles. The RPA calculations shown here were convoluted with a Gaussian instrument resolution function using an elastic energy resolution of $\Delta E=1\text{meV}$ and a transverse $Q$ resolution of $\Delta Q\sim 0.06{\text{Å}}^{-1}$.

Figure 3

(Color online) (a) Experimental dispersions of the magnetic excitations of ${\text{FeTe}}_{0.6}{\text{Se}}_{0.4}$ at 20 and 2 K determined by fitting Gaussian peaks to the measured excitations. A linear fit to the 20 K data is illustrated as a red lines. The horizontal errors bars indicate the full width at half maximum of the excitation determined from a fit of a Gaussian to the data. (b) Dispersion of the incommensurate spin resonance as determined from difference transverse INS scans through $\mathbf{Q}=\left(1/2,1/2\right)$ at various energy transfers between 6 and 12 meV. The difference is modeled using two Gaussians centered on incommensurate positions and the fit is shown as a continuous line through the data. For 6 meV data we shown the two individual peaks as dashed lines.