Site dilution and charge disorder effect on physical properties in SrRu$_{1-x}$Ga$_x$O$_3$

Here, we report an evolution of structural, magnetic and transport behavior in doped SrRu$_{1-x}$Ga$_x$O$_3$ ($x$ $\le$ 0.2). The nonmagnetic dopant Ga$^{3+}$ (3$d^{10}$) not only acts for magnetic site dilution in SrRuO$_3$ but also it modifies the Ru charge state and electronic density. Our studies show that Ga$^{3+}$ substitution does not affect the original orthorhombic-\textit{Pbnm} structure of SrRuO$_3$ which is due to its matching ionic radii with Ru$^{4+}$. However, Ga$^{3+}$ has a substantial effect on the magnetic behavior of SrRuO$_3$ where it decreases both magnetic moment as well as magnetic transition temperature $T_c$. Further, this dilution induces Griffiths phase behavior across $T_c$ and cluster-glass behavior at low temperature with higher concentration of doping. The magnetic critical exponent $\beta$ increases with $x$ due to this site dilution effect. The Ga$^{3+}$ induces an insulating state in SrRuO$_3$ with $x$ $>$ 0.05. The charge transport in paramagnetic as well as in insulating state of samples can be well described with Mott's modified variable-range-hopping model. The metallic charge transport just below $T_c$ in SrRuO$_3$ obeys Fermi liquid behavior which, however breaks down at low temperature. We further find a correlation between field dependent magnetoresistance and magnetization through power-law behavior over the series.