We have performed muon spin relaxation ($\mu \mathrm{SR}$) and neutron powder diffraction experiments on the ferromagnet ${\mathrm{Sr}}_{1-x}$(${\mathrm{La}}_{0.5}{\mathrm{K}}_{0.5}{)}_x{\mathrm{RuO}}_3$. ${\mathrm{SrRuO}}_3$ shows a ferromagnetic (FM) order below 160 K, and the FM ordering temperature is monotonically suppressed as $x$ increases, eventually vanishing at the critical concentration $x_{\mathrm{c}}$ = 0.5. During this suppression process, the FM ordered state evolves into an FM cluster-glass state for $x \ge$ 0.4. Neutron scattering intensity due to the FM order develops below the magnetic ordering temperatures, but no antiferromagnetic peaks have been observed in either the FM or cluster-glass states within the experimental accuracy. The internal field at lowest temperatures revealed by the $\mu \mathrm{SR}$ experiments is monotonically suppressed as $x$ increases. In contrast, the magnetic volume fraction $V_{\mathrm{f}}$ at lowest temperatures decreases only moderately with $x$ up to $x$ = 0.3, but drops rapidly near the critical concentration. The fact that $V_{\mathrm{f}}$ is less than 1 for $x \ge$ 0.3 is expected to be related to the origin of the cluster-glass state formation. We also found that the muon relaxation rate due to magnetic fluctuations in the cluster-glass state increases as $x$ approaches $x_{\mathrm{c}}$, reflecting progressive destabilization of the cluster-glass state due to the reduction of $V_{\mathrm{f}}$. These results indicate that the magnetically ordered states of ${\mathrm{Sr}}_{1-x}$(${\mathrm{La}}_{0.5}{\mathrm{K}}_{0.5}{)}_x{\mathrm{RuO}}_3$ are strongly affected by the disorder effect, and the suppression process of the FM order is largely different from that in a clean system. We compare the present experimental results with those for other Sr-site substituted systems, and discuss the differences in their magnetic properties and how they are affected by the disorder effect.

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• Ferromagnetism
• Strongly correlated systems
• Transition metal oxides
• Muon spin relaxation & rotation
• Neutron diffraction