We demonstrate that the cluster-glass state emerges as ferromagnetic quantum criticality is avoided in itinerant ferromagnet Sr${}_{1-x}$(La${}_{0.5}$K${}_{0.5}$)${}_x$RuO${}_3$. 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 SrRuO${}_3$, and suggest that a local correlated disorder effect and the very small coherence of itinerant Ru 4$d$ electrons are responsible for the cluster-glass formation instead of the quantum phase transition in Sr${}_{1-x}$(La${}_{0.5}$K${}_{0.5}$)${}_x$RuO${}_3$.

中文翻译：

---

避免了迭代铁磁体Sr1-x（La0.5K0.5）xRuO3中的量子临界和团簇玻璃形成

我们证明了簇玻璃状态的出现是因为在迭代铁磁体Sr中避免了铁磁量子临界${}_{\mathrm{1个}-X}$（拉${}_{0.5}$ķ${}_{0.5}$）${}_X$O${}_3$。在该化合物中，通过增加铁磁序来抑制$X$，然后在临界浓度下消失： $X=0.5$。在这个$X$在此范围内，本研究表明没有明显的特征归因于比热的量子临界波动。取而代之的是，由于自发的自旋冻结，交流磁化率显示出一个宽的峰值，并且峰值温度明显取决于所施加的交流磁场的频率。此外，比热在较宽的温度范围内得到增强，而比热显示没有与旋转冻结相关的显着异常。这些特征是团簇玻璃形成的特征。尤其是，所观察到的交流磁化率的频率变化已由Vogel-Fulcher定律很好地描述了。我们比较了这种掺杂化合物与同构Ca和La掺杂SrRuO中的铁磁有序抑制特征。${}_3$，并表明局部相关的紊乱效应和流动性Ru 4的非常小的相干性$d$ 电子负责团簇玻璃的形成，而不是Sr中的量子相变${}_{\mathrm{1个}-X}$（拉${}_{0.5}$ķ${}_{0.5}$）${}_X$O${}_3$。