Friedel-like Oscillations from Interstitial Iron in Superconducting Fe$_{1+y}$Te$_{0.62}$Se$_{0.38}$*

Using polarized and unpolarized neutron scattering we show that interstitial Fe in superconducting Fe$_{1+y}$Te$_{1-x}$Se$_x$ induces a magnetic Friedel-like oscillation that diffracts at ${\bf Q}_{\perp}=(\frac{1}{2}0)$ and involves $>$50 neighboring Fe sites. The interstitial $>2$~$\mu_B$ moment is surrounded by compensating ferromagnetic four spin clusters that may seed double stripe ordering in Fe$_{1+y}$Te. A semi-metallic 5-band model with $(\frac{1}{2}\frac{1}{2})$ Fermi surface nesting and four fold symmetric super-exchange between interstitial Fe and two in-plane nearest neighbors largely accounts for the observed diffraction.