Carrier doping to the Mott insulator is essential to produce highly correlated metals with emergent properties. The pyrochlore ruthenates ${\mathrm{Pr}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ (Ru $4d$ electron number $n=4$) and ${\mathrm{Ca}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ ($n=3$) are a Mott insulator and a magnetic bad metal, respectively, due to the strong electron correlation. We investigate magnetotransport properties of ${\left({\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x\right)}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ in a whole band-filling range, $0\le x\le 1$. With increasing hole doping $x$, the system undergoes an insulator-metal transition. When ${\mathrm{Ca}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ is doped with electrons ($0.5<x<0.9$), the enhanced coupling among Ru $4d$ spins produces a ferromagnetic-metal phase with a large anomalous-Hall angle up to 2%. We discuss the electronic phase transitions in ${\left({\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x\right)}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ in view of Hund's metal.

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• Anomalous Hall effect
• Metal-insulator transition
• Mott insulators
• Ruthenates