Magnetism and its interplay with Superconductivity in the Doped Iron Chalcogenide Fe$_{\mathrm{1+y}}$Te$_{\mathrm{1-x}}$Se$_{\mathrm{x}}$

I examine the relationship of iron superconductivity with impurities, and low energy magnetic excitations in the structurally simple iron superconductor, (Fe$_{\mathrm{1+y}}$Te$_{\mathrm{1-x}}$Se$_{\mathrm{x}})$. In the first part of the talk, the pivotal role played by interstitial iron impurities in the microscopic origin of the quasi-static magnetism at (1/2,0) is demonstrated in Fe$_{\mathrm{1+y}}$Te$_{0}$ 0.38 [1]. We used polarized and unpolarized neutron scattering together with simulations of the scattering function based on structural data and a semi-metallic 5-band model with super-exchange interactions with the interstitial iron, to show that the formation of magnetic polarons around the interstitial iron atoms seeds the observed (1/2,0) magnetism. Though the quasi-static magnetism occurs at (1/2,0), the low energy spin dynamics are dominated by fluctuations at (1/2,1/2), like other iron based superconductors. In the second part of the talk, I will discuss these fluctuations and in particular the so-called spin resonance -- the signature feature in the low energy inelastic neutron scattering spectrum. We show that this scattering is quasi two dimensional and largely isotropic. Further, the first moment sum-rule for the dynamic correlation function is applied to the inelastic data in the normal and superconducting states to quantitatively determine the magnetic component of the superconducting condensation energy [2]. This method is sensitive to changes in the inter-site magnetic correlation energy, $\Delta $Eij, associated with superconductivity. We find that the length scale over which $\Delta $Eij is appreciable is similar to the superconducting coherence length, as determined by Scanning Tunneling Microscopy. Comparison of the inter-site magnetic correlation energy to the superconducting condensation energy determined through specific heat measurements indicates a significant role of magnetic fluctuations in stabilizing superconductivity. \\[4pt] [1] V. Thampy et al, Phys. Rev. Lett. 108, 107002 (2012).\\[0pt] [2] J. Leiner et al, Manuscript under preparation.