Charge-ordered states in (La,Sr${)}_2$${\mathrm{NiO}}_4$ for hole concentrations ${\mathit{n}}_{\mathit{h}}$=1/3 and 1/2

Real-space ordering of doped holes in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{NiO}}_4$ is revealed in magnetic and electronic-transport anomalies at low temperatures. The ordering is most pronounced for a hole concentration ${\mathit{n}}_{\mathit{h}}$ of 1/3 below 235 K where a superlattice with a modulation wave vector δ of 1/3 has been found. For ${\mathit{n}}_{\mathit{h}}$=1/2, another charge-ordered state with δ=0 is also indicated below ∼340 K. Our results are, furthermore, suggestive of mesoscopic hole segregation for 0.2≤x≤0.4 forming the ${\mathit{n}}_{\mathit{h}}$=1/3 and δ=1/3 state below 235 K.