  The evolution of the electronic properties of electron-doped
(Sr{1-x}La{x})2IrO4 is experimentally explored as the doping limit of La is
approached. As electrons are introduced, the electronic ground state
transitions from a spin-orbit Mott phase into an electronically phase separated
state, where long-range magnetic order vanishes beyond x = 0.02 and charge
transport remains percolative up to the limit of La substitution (x~0.06). In
particular, the electronic ground state remains inhomogeneous even beyond the
collapse of the parent state's long-range antiferromagnetic order, while
persistent short-range magnetism survives up to the highest La-substitution
levels. Furthermore, as electrons are doped into Sr2IrO4, we observe the
appearance of a low temperature magnetic glass-like state intermediate to the
complete suppression of antiferromagnetic order. Universalities and differences
in the electron-doped phase diagrams of single layer and bilayer
Ruddlesden-Popper strontium iridates are discussed.
