Temperature and doping-level dependence of magnetic order in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_{4+\delta }$ studied by muon spin rotation

We report muon-spin-rotation $(\mu$SR) measurements on a series of compounds with composition ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_{4+\delta }$ with strontium doping level x between 0 and 1. A magnetic transition is found in all the samples studied, which occurs at a composition-dependent temperature, $T_M.$ Below $T_M$ clear precession signals are observed in zero applied magnetic field for all $x$, indicating the existence of at least short-range magnetic order on a time scale longer than ${10}^{-8}$ s. Above $T_M$ the magnetic correlation times decrease by several orders of magnitude. At $x\approx 0.33$, we find peaks in both $T_M$ and the zero-temperature staggered magnetization, an observation which we attribute to the higher degree of localization of the holes at this doping level. The measurements of $T_M$ as a function of x extend the determination of Néel temperatures by previous neutron diffraction and $\mu$SR measurements.