Modified magnetism within the coherence volume of superconducting ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$

Neutron scattering is used to probe magnetic interactions as superconductivity develops in optimally doped ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$. Applying the first moment sum rule to comprehensive neutron scattering data, we extract the change in magnetic exchange energy $\Delta \left[J_{\mathbf{R}-{\mathbf{R}}^{\prime }}\langle {\mathbf{S}}_{\mathbf{R}}·{\mathbf{S}}_{{\mathbf{R}}^{\prime }}\rangle \right]$ in the superconducting state referenced to the normal state. Oscillatory changes are observed for Fe-Fe displacements $\left|\Delta \mathbf{R}\right|<\xi$, where $\xi =1.3\left(1\right)$ nm is the superconducting coherence length. Dominated by a large reduction in the second nearest neighbor exchange energy [$-1.2\left(2\right)$ meV/Fe], the overall reduction in magnetic interaction energy is $\Delta \langle {\mathcal{H}}_{\text{mag}}\rangle =-0.31\left(9\right)$ meV/Fe. Comparison to the superconducting condensation energy $\Delta E_{\text{SC}}=-0.013\left(1\right)$ meV/Fe, which we extract from specific heat data, suggests the modified magnetism we probe drives superconductivity in ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$.

Figure 1

Inelastic neutron scattering data for ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$ weighted by energy transfer. In the left column, (a) and (b) show $\hslash \omega (1-exp(-\beta \hslash \omega ))\mathcal{S}(\mathbf{Q},\omega )$ for wave vector transfer along the high symmetry directions indicated in (d) and measured on the ARCS instrument at ORNL for $x=0.49$ at $T=4$ and 25 K, respectively. In the right column, (d) and (e) show $\mathcal{E}\left(\mathbf{Q}\right)$ [Eq. (3)] integrated from $1\mathrm{meV}<\hslash \omega <11\mathrm{meV}$ for $x=0.4$ measured on MACS at NIST at $T=1.4$ and $25\mathrm{K}$, respectively. (c) and (f) show the difference between superconducting and normal state data. Note that harmonic phonon scattering visible in (a) and (b) and (d)–(e) cancels in the subtraction. For presentation purposes, each pixel reports the average of the raw intensity in an area of dimensions of (0.05 r.l.u.)${}^2$.

Figure 2

Plot of $\Delta \mathcal{E}\left(\mathbf{Q}\right)$ which may be interpreted as the momentum resolved difference in magnetic exchange energy [Eq. (6)]. All data has been projected to a single octant of the Brillouin zone. Data for different choices of upper cutoff $E_2$ are shown for $K>H$ and $K<H$. Actual data are shown for $K<1-H$, whereas the $K>1-H$ region is a Fourier reconstruction [Eq. (3)] with a cutoff length scale $\Delta R=4a$. For presentation purposes, each pixel reports the average of the raw intensity in an area of dimensions of (0.05 r.l.u.)${}^2$.

Figure 3

The change in bond energy vs bond length derived via Eq. (5). The vertical line indicates the SC coherence length with an error bar as extracted from scanning tunneling microscopy (STM). The inset shows a graphical representation of the bond vectors within the coherence length (yellow ring). The area of the circles indicates the magnitude of the change in bond energy through the SC transition, and the color red (blue) indicates an energy increase (decrease).

Figure 4

(a) Specific heat measurements and the associated entropy for ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$ samples. (b) Condensation energy vs temperature derived from (a), as described in the text.