Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate Eu_{2}Ir_{2}O_{7}.

We report a resonant inelastic x-ray scattering study of the magnetic excitation spectrum in a highly insulating Eu_{2}Ir_{2}O_{7} single crystal that exhibits a metal-insulator transition at T_{MI}=111(7)  K. A propagating magnon mode with a 20 meV bandwidth and a 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in-all-out magnetically ordered state. This magnetic excitation exhibits substantial softening as the temperature is raised towards T_{MI} and turns into a highly damped excitation in the paramagnetic phase. Remarkably, the softening occurs throughout the whole Brillouin zone including the zone boundary. This observation is inconsistent with the magnon renormalization expected in a local moment system and indicates that the strength of the electron correlation in Eu_{2}Ir_{2}O_{7} is only moderate, so that electron itinerancy should be taken into account in describing its magnetism.