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We demonstrate that the cluster-glass state emerges as ferromagnetic quantumcriticality is avoided in itinerant ferromagnet Sr1-x(La0.5K0.5)xRuO3. In thiscompound, the ferromagnetic order is suppressed by increasing x, and thendisappears at the critical concentration: x=0.5. In this x range, the presentstudy reveals that no prominent feature is ascribed to the quantum criticalfluctuations in specific heat. Instead, ac magnetic susceptibility exhibits abroad peak due to spontaneous spin freezing, and the peak temperature dependssignificantly on the frequency of the applied ac magnetic field. Furthermore,specific heat is enhanced within a wide temperature range, whereas specificheat shows no salient anomaly associated with spin freezing. These features arecharacteristics of the formation of cluster-glass; in particular, the observedfrequency variations in ac magnetic susceptibility are well described by theVogel-Fulcher law. We compare the features concerning the suppression of theferromagnetic order in this doped compound with those in isostructural Ca- andLa-doped SrRuO3, and suggest that a local correlated disorder effect and thevery small coherence of itinerant Ru 4d electrons are responsible for thecluster-glass formation instead of the quantum phase transition inSr1-x(La0.5K0.5)xRuO3.

Avoided quantum criticality and cluster-glass formation in itinerant ferromagnet Sr$_{1-x}$(La$_{0.5}$K$_{0.5}$)$_x$RuO$_3$