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We report the results of a muon-spin relaxation ($\mu$SR) investigation ofLa$_{2-x}$Sr$_{x}$CoO$_{4}$, an antiferromagnetic insulating series which hasbeen shown to support charge ordered and magnetic stripe phases and anhourglass magnetic excitation spectrum. We present a revised magnetic phasediagram, which shows that the suppression of the magnetic ordering temperatureis highly sensitive to small concentrations of holes. Distinct behavior withinan intermediate $x$ range ($0.2 \leq x \lesssim 0.6$) suggests that theputative stripe ordered phase extends to lower $x$ than previously thought.Further charge doping ($0.67 \leq x \leq 0.9$) prevents magnetic ordering for$T \gtrsim 1.5~{\rm K}$

Magnetic phase diagram of La$_{2-x}$Sr$_{x}$CoO$_{4}$ revised using muon-spin relaxation