Title: Evolution of ferrimagnetism against Griffiths singularity in Calcium Ruthenate

Abstract: The magnetism in the correlated metal CaRuO$_3$ is enigmatic as it is poised near a triple point among the ferromagnetic, antiferromagnetic, and paramagnetic ground states. Here we report a detailed work on structural, spectroscopic, magnetic, and transport properties in CaRu$_{1-x}$Cr$_x$O$_3$. We find that Cr doping reduces the orthorhombicity in CaRuO$_3$. Surprisingly, a tiny (x = 0.01) amount of Cr-doping drives the magnetic ground state from \enquote{paramagnetic-like} to ferrimagnetic. Slightly higher Cr-doping (x = 0.05) results formation of magnetic clusters which gives rise to Griffiths singularity and power law divergence in magnetic susceptibility. The magnetism in CaRu$_{1-x}$Cr$_x$O$_3$ is explained in terms of \enquote{seven atom} ferrimagnetic clusters. Electrical transport shows a gradual evolution of a non-metallic state upon Cr-doping. In particular, for x $\geq$ 0.1, the temperature-dependent resistivity follows Mott-VRH conduction. The XPS study also supports significant role of disorder and electron correlation which effectively reduces the itinerant character of electrons. Finally, a new T-x phase diagram is constructed depicting the evolution of electronic and magnetic state in CaRu$_{1-x}$Cr$_x$O$_3$.