Common origin of the two types of magnetic fluctuations in iron chalcogenides

We use inelastic neutron scattering to study the low-energy spin excitations in moderately doped nonsuperconducting Fe${}_{1.01}$Te${}_{0.72}$Se${}_{0.28}$. The spin excitations in this system contain components near (0.5,0,0) and (0.5,0.5,0) in a-b plane reciprocal lattice units using tetragonal unit cell notation ($a=b=3.772$ Å and $c=6.061$ Å). At low energies the scattering is centered around (0.5,0,0). With increasing energy, the spectral weight of low-energy spin excitations centered around (0.5,0,0) abruptly shifts around 3 meV to the incommensurate spin excitations centered around (0.5,0.5,0). However both types of spin fluctuations exhibit the identical temperature dependence. These results indicate that the (0.5,0,0)-type spin excitations and the incommensurate excitations around the (0.5,0.5,0) position have a common origin and both must be taken into account to understand the nature of magnetism and superconducting pairing in the iron chalcogenides.

Figure 1

(a) The schematic $C$-type collinear AFM order of the Fe moments in the a-b plane for iron pnictides such as LaFeAsO.[41] The shaded area represents the tetragonal unit cell which is used in the study. (b) The a-b-plane projection of the $E$-type bicollinear AFM spin structure for iron telluride FeTe. (c) Schematic of the observed spin excitations for Se-doped FeTe in reciprocal space. The red star shows the position where FS nesting occurs and the spin resonance has been observed for both pnictides and chalcogenides. The solid blue circles represent the low-energy spin fluctuations at (0.5,0,0) and the filled green ellipses show the ICM excitations centered around the (0.5,0.5,0) position. (d) Temperature dependence of the integrated intensity of scans along ($H,0,0.5$) taken on BT-7. The inset shows the background-subtracted $H$ scans at some typical temperatures. (e) Constant-$\mathbf{Q}$ scans at (0.5,0.5,0) measured on SPINS at $T=1.4$ K and $T=20$ K. There is no evidence of a spin resonance or the development of a spin gap.

Figure 2

Contour plots of neutron scattering intensity in the $(H,K,0)$ plane at energy transfers of (a) 1.5 meV (b) 3.5 meV, (c) 4.5 meV, (d) 6.0 meV, (e) 7.0 meV, and (f) 8.0 meV. The data were collected at $T=1.5$ K on MACS. All the panels are plotted with the same color scale to show the intensity variations. The arrows in (a) and (b) show the directions of constant-$E$ cuts plotted in Fig. 3.

Figure 3

Contour plot of combined cuts for the $T=1.5$ K data in the (a) $[0.5,K]$ direction and (b) the $[H,1-H]$ direction through (0.5,0.5) as a function of energy. Both figures are plotted on the same energy scale so that the correspondence between the two excitations can be seen. The open circle data in (b) are the result of a two-Gaussian fit to the peaks shown in Fig. 5a, which are measured using the high-resolution configuration on SPINS.

Figure 4

(a) Constant-Q cut along $E$ at (0.5,0) [black solid squares] and (1,0.5) [blue solid circles]. (b) Cut at (0.5,0.5) along $E$. The dashed line shows roughly where the abrupt changes of intensities occur. (c) Integrated intensity of the cut through (0.5,0) along the $H$ direction with background subtracted. The inset shows the linewidth of the (0.5,0) excitation cut along the K direction.(d) The sum of fitted areas of the two peaks from the transverse scan through (0.5,0.5). Data obtained from BT-7 are used for $\mathit{\text{E}}\ge 8$ meV.

Figure 5

Typical scans along the [$H,1-H$] direction at various energy transfers carried out on (a) SPINS and (b) BT-7 at $T=1.5$ K. The lines are Gaussian least squares fits convoluted with instrument resolution. The intensities and fits are shifted up sequently by an equal amount between adjacent scans for clarity.

Figure 6

Temperature dependence of the cut (a) along [0.5,K] at $E$ $=$ 1 meV and (b) along [$H,1-H$] at $E$ $=$ 1 meV and (d) $E$ $=$ 10 meV. Note the change made in the vertical color bar scales to better show the change of intensities. (c) Temperature dependence of the full-width-at-half-maximum (FWHM) of the (0.5,0) spectrum at $E$ $=$ 1 meV.

Figure 7

Temperature dependence of the integrated intensities of (a) the (0.5,K) scan at $E$ $=$ 1 meV and $E$ $=$ 4.5 meV, and (b) the $[H,1-H]$ scan through (0.5,0.5) at $E$ $=$ 1 meV, 4.5 meV, 7 meV, and 10 meV. (c) Temperature dependence of the dynamic susceptibility in the paramagnetic phase ($60\text{K}<T<310\text{K}$) obtained from the (0.5,0) type of excitations and (d) the (0.5,0.5) ICM excitations. The lines in (c) and (d) are fits to the power law ${\chi }^{\prime \prime }=C{T}^{\beta }$.