Critical behavior in itinerant ferromagnet SrRu$_{1-x}$Ti$_x$O$_3$

SrRuO$_3$ presents a rare example of ferromagnetism among the 4$d$ based oxides. While the nature of magnetic state in SrRuO$_3$ is mostly believed to be of itinerant type, recent studies suggest a coexistence of both itinerant and localized model of magnetism in this material. Here, we have investigated the evolution of magnetic state in doped SrRu$_{1-x}$Ti$_x$O$_3$ through studying the critical behavior using standard techniques such as, modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis across the magnetic transition temperature $T_c$. The substitution of nonmagnetic Ti$^{4+}$ (3$d^{0}$) for Ru$^{4+}$ (4$d^4$) would simply dilute the magnetic system apart from modifying the electron correlation effect and the density of states at Fermi level. Surprisingly, $T_c$ does not change with $x$. Moreover, our analysis show the exponent $\beta$ related to spontaneous magnetization increases while the exponents $\gamma$ and $\delta$ related to initial inverse susceptibility and critical magnetization, respectively decrease with Ti substitution. The estimated exponents do not match with any established theoretical models for universality classes, however, the exponent obey the Widom relation and the scaling behavior. Interestingly, this particular evolution of exponents in present series has similarity with that in isoelectronic doped Sr$_{1-x}$Ca$_x$RuO$_3$. We believe that site dilution by Ti leads to formation magnetic clusters which causes this specific changes in critical exponents.