Abstract
Iron based high temperature superconductors have several common features with superconducting cuprates, including the square lattice and the proximity to an antiferromagnetic phase. The magnetic excitation spectrum below Tc of shows an hourglass-shaped dispersion with a resonance around the commensurate point . In a previous inelastic neutron scattering study, we showed that the hourglass-shaped dispersion is most likely a prerequisite for superconductivity, while the consequences are the opening of a gap and a shift of spectral weight. In this paper we follow the evolution of the hourglass shaped dispersion under applied pressure up to 12 kbar. Our results show that that the pressure-induced 37% increase of Tc is concomitant with a change in the magnetic excitation spectrum, with an increase of the hourglass energy by 38%.