Disordered dimer state in electron-doped Sr$_{3}$Ir$_{2}$O$_{7}$

Spin excitations are explored in the electron-doped spin-orbit Mott insulator (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$. As this bilayer square lattice system is doped into the metallic regime, long-range antiferromagnetism vanishes, yet a spectrum of gapped spin excitation remains. Excitation lifetimes are strongly damped with increasing carrier concentration, and the energy integrated spectral weight becomes nearly momentum independent as static spin order is suppressed. Local magnetic moments, absent in the parent system, grow in metallic samples and approach values consistent with one $J=\frac{1}{2}$ impurity per electron doped. Our combined data suggest that the magnetic spectra of metallic (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$ are best described by excitations out of a disordered dimer state.