Magnetic hour-glass dispersion and its relation to high-temperature   superconductivity in iron-tuned Fe$_{1+y}$Te$_{0.7}$Se$_{0.3}$
  High-temperature superconductivity remains arguably the largest outstanding enigma of condensed matter physics. The discovery of iron-based high-temperature superconductors has renewed the importance of understanding superconductivity in materials susceptible to magnetic order and fluctuations. Intriguingly they show magnetic fluctuations reminiscent of the superconducting (SC) cuprates, including a 'resonance' and an 'hour-glass' shaped dispersion, which provide an opportunity to new insight to the coupling between spin fluctuations and superconductivity. Here we report inelastic neutron scattering data on Fe$_{1+y}$Te$_{0.7}$Se$_{0.3}$ using excess iron concentration to tune between a SC ($y=0.02$) and a non-SC ($y=0.05$) ground states. We find incommensurate spectra in both samples but discover that in the one that becomes SC, a constriction towards a commensurate hourglass shape develop well above $T_c$. Conversely a spin-gap and concomitant spectral weight shift happen below $T_c$. Our results imply that the hourglass shaped dispersion is most likely a pre-requisite for superconductivity, whereas the spin-gap and shift of spectral weight are consequences of superconductivity. We explain this observation by pointing out that an inwards dispersion towards the commensurate wave-vector is needed for the opening of a spin gap to lower the magnetic exchange energy and hence provide the necessary condensation energy for the SC state to emerge. 
N. Tsyrulin, R. Viennois, E. Giannini, M. Boehm, M. Jimenez-Ruiz, A.   A. Omrani, B. Dalla Piazza and H. M. Ronnow
cond-mat.supr-con cond-mat.str-el