Coupling of spin and orbital excitations in the iron-based superconductor ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$

We present a combined analysis of neutron scattering and photoemission measurements on superconducting ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$. The low-energy magnetic excitations disperse only in the direction transverse to the characteristic wave vector $\left(\frac{1}{2},0,0\right)$ whereas the electronic Fermi surface near $\left(\frac{1}{2},0,0\right)$ appears to consist of four incommensurate pockets. While the spin resonance occurs at an incommensurate wave vector compatible with nesting, neither spin-wave nor Fermi-surface-nesting models can describe the magnetic dispersion. We propose that a coupling of spin and orbital correlations is key to explaining this behavior. If correct, it follows that these nematic fluctuations are involved in the resonance and could be relevant to the pairing mechanism.

Figure 1

(Color online) (a) Atomic positions within an Fe plane of ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$. Filled (open) diamonds indicate Se/Te atoms that sit above (below) the plane. Solid line: unit cell used here; dashed line: crystallographic unit cell. (b) Spin pattern corresponding to $\mathbf{Q}=\left(\frac{1}{2},0\right)$. (c) Reciprocal space corresponding to (a) with symmetry point labeled. Solid line: Brillouin zone for one Fe per unit cell; dashed line: Brillouin zone for two Fe per unit cell. (d) Reciprocal space labeled in reciprocal lattice units, indicating directions of scans for the neutron scattering measurements.

Figure 2

(Color) (a) ARPES intensity map at $E_F$, integrated over 0–10 meV binding energy; upper half measured at the ALS with 50-eV photons and lower half from the NSLS with 17-eV photons. Thick red lines indicate estimated Fermi-surface positions; thin red lines denote pockets inferred by symmetry. Red arrows denote polarization direction; at (0, 0.5) polarization has a $k_z$ component that varies with $k_x$. (b) Intensity map ($\text{white}=\text{minimum}$, $\text{blue}=\text{maximum}$) along line denoted as Cut A in (a). Red dots indicate positions of bands as they cross $E_F$. Asymmetry about $k_y=0$ is due to imperfect sample orientation. (c) Calculated spectral weight at $E_F$, averaged over $k_z$. Orbital coding: red—$d_{yz}$; blue—$d_{xz}$; and green—all others. (d) Calculated band dispersions along symmetry directions with intensity scaled according to spectral weight, obtained by unfolding bands calculated in a reduced zone (Ref. 22); color code same as (c).

Figure 3

(Color online) Momentum dependence of the spin resonance and low-energy spin fluctuations. (a) Inelastic neutron-scattering intensity as a function of $\mathbf{Q}$, obtained with constant energies, 8, 6.5, 5, and 4 meV, at 1.5 K $\left(<T_c\right)$ [open (red) circles] and 20 K $\left(>T_c\right)$ [filled (blue) circles], taken along the transverse $\left(0.5,k\right)$ direction. The lines are fits to Gaussians; diamonds (open, 1.5 K; filled, 20 K) indicate fitted peak positions. Horizontal bars represent the full width of the half maximum of the instrumental $Q$ resolution. (b) Color contour map summarizing 1.5-K data obtained from a series of $\left(0.5,k\right)$ scans centered at positions marked by red squares. (c) Dispersion of the spin fluctuations. Open green squares extending to high energies are taken from Ref. 24 while open red diamonds (1.5 K) and filled blue diamonds (20 K0 at low energies are our data taken from (a); horizontal bars are fitted peak widths at the lowest energies and $T=20\text{K}$. The line is explained in the text.

Figure 4

(Color online) (a) Cartoon of $\text{spin}+\text{orbital}$ flip excitation discussed in text, assuming finite-range spin and orbital correlations. Vertical (horizontal) line denotes $d_{yz}$ $\left(d_{xz}\right)$ orbital. (b) Form factor for the excitation in (a). Color map: low-medium-$\text{high}=\text{blue}$-green-red (dark-light-gray). (c) Cartoon of intersite spin-flip excitation. (d) Form factor map for the excitation in (c).