We report the results of a muon-spin relaxation (μSR) investigation of La 2−x Sr x CoO 4 , an antiferromagnetic insulating series which has been shown to support charge ordered and magnetic stripe phases and an hourglass magnetic excitation spectrum. We present a revised magnetic phase diagram, which shows that the suppression of the magnetic ordering temperature is highly sensitive to small concentrations of holes. Distinct behavior within an intermediate x range (0.2 x 0.6) suggests that the putative stripe ordered phase extends to lower x than previously thought. Further charge doping (0.67 x 0.9) prevents magnetic ordering for T 1.5 K.DOI: 10.1103/PhysRevB.93.140406Thirty years after the discovery of high-T c superconductivity, the role of multiple order parameters in the cuprates continues to be a topic of intense research, with the interplay between correlations of charge order (CO), antiferromagnetic spin order (SO), and superconductivity the topic of much investigation [1][2][3][4][5]. Although a detailed comparison of specific systems has been found to be problematical, in order to elucidate the details of the physics at play in a different context it is illuminating to study isostructural nonsuperconducting 3d transition metal oxides [6] such as the antiferromagnetic series La 2−x Sr x CoO 4 (LSCO). Controlled doping of holes into the two-dimensional CoO 2 layers is achieved via substitution of Sr for La but, in contrast to the cuprates, a spin-blockade mechanism means the series remains an insulator for x 1 [7]. The previously reported phase diagram of LSCO, determined by neutron scattering [8], shows a region of nearest-neighbor antiferromagnetism (nnAFM) for low dopant concentrations (x 0.3) and incommensurate (IC) magnetism consistent with stripelike CO and SOs for an intermediate doping range 0.3 x 0.6. Recently, muon-spin rotation (μSR) and NMR measurements made on the stripe ordered x = 1/3 compound [9] revealed the importance of a range of time scales in the magnetic ordering of the material, with μSR showing both the onset of static magnetic order and the freezing of dynamical processes at temperatures significantly lower than the ordering temperature previously identified using neutrons. This is because μSR is sensitive to fluctuations on the microsecond time scale (set by the muon gyromagnetic ratio γ μ = 2π × 135.5 MHz T −1 ). Such slow fluctuations appear static in neutron scattering measurements where the energy resolution E ≈ 1 meV constrains the sensitivity of the technique to fluctuations with a much faster time scale