Effect of magnetic field on the spin resonance in FeTe$_{0.5}$Se$_{0.5}$ as seen via inelastic neutron scattering

Inelastic neutron scattering and susceptibility measurements have been performed on the optimally-doped Fe-based superconductor FeTe$_{0.5}$Se$_{0.5}$, which has a critical temperature, $T_c$ of 14~K. The magnetic scattering at the stripe antiferromagnetic wave-vector ${\bf Q}=(0.5,0.5)$ exhibits a ``resonance'' at $\sim6$~meV, where the scattering intensity increases abruptly when cooled below $T_c$. In a 7-T magnetic field, $T_c$ is slightly reduced to $\sim12$~K, based on susceptibility measurements. The resonance in the neutron scattering measurements is also affected by the field applied along the [1$\bar1$0] direction. The resonance intensity under field cooling starts to rise at a lower temperature $\sim12$~K, and the low temperature intensity is also reduced from the zero-field value. Our results provide clear evidence for the intimate relationship between superconductivity and the resonance measured in magnetic excitations of Fe-based superconductors.