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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 isdoped into the metallic regime, long-range antiferromagnetism vanishes, yet aspectrum of gapped spin excitation remains. Excitation lifetimes are stronglydamped with increasing carrier concentration, and the energy integratedspectral weight becomes nearly momentum independent as static spin order issuppressed. Local magnetic moments, absent in the parent system, grow inmetallic samples and approach values consistent with one $J=\frac{1}{2}$impurity per electron doped. Our combined data suggest that the magneticspectra of metallic (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$ are best described byexcitations out of a disordered dimer state.

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