  We demonstrate that the cluster-glass state emerges as ferromagnetic quantum
criticality is avoided in itinerant ferromagnet Sr1-x(La0.5K0.5)xRuO3. In this
compound, the ferromagnetic order is suppressed by increasing x, and then
disappears at the critical concentration: x=0.5. In this x range, the present
study reveals that no prominent feature is ascribed to the quantum critical
fluctuations in specific heat. Instead, ac magnetic susceptibility exhibits a
broad peak due to spontaneous spin freezing, and the peak temperature depends
significantly on the frequency of the applied ac magnetic field. Furthermore,
specific heat is enhanced within a wide temperature range, whereas specific
heat shows no salient anomaly associated with spin freezing. These features are
characteristics of the formation of cluster-glass; in particular, the observed
frequency variations in ac magnetic susceptibility are well described by the
Vogel-Fulcher law. We compare the features concerning the suppression of the
ferromagnetic order in this doped compound with those in isostructural Ca- and
La-doped SrRuO3, and suggest that a local correlated disorder effect and the
very small coherence of itinerant Ru 4d electrons are responsible for the
cluster-glass formation instead of the quantum phase transition in
Sr1-x(La0.5K0.5)xRuO3.
