Determination of a Magnetic Component to the Superconducting Condensation Energy for Fe$_{\mathrm{1+\delta }}$Se$_{\mathrm{x}}$Te$_{\mathrm{1-x}}$*

A quantitative method to extract a magnetic component of the superconducting condensation energy from inelastic neutron scattering data is described and applied to Fe$_{\mathrm{1+\delta }}$Se$_{\mathrm{0.4}}$Te$_{\mathrm{0.6}}$. Based on the first moment sum-rule for the dynamic correlation function, the method is sensitive to changes in the inter-site magnetic correlation energy, $\Delta E_{\mathrm{ij}}$, associated with superconductivity. We find the length scale over which $\Delta E_{\mathrm{ij\thinspace }}$is appreciable coincides with the superconducting coherence length as determined by Scanning Tunneling Microscopy. The overall change in inter-site magnetic correlation energy is compared to the superconducting condensation energy determined through specific heat measurements.