Effect of disorder on quantum phase transition in (Sr$_{1-x}$Ca$_x$)$_3$Ru$_2$O$_7$

(Sr$_{1-x}$Ca$_{x}$)$_{3}$Ru$_{2}$O$_{7}$ is characterized by complex magnetic states, spanning from anantiferromagnetic state over an unusual heavy-mass nearly ferromagnetic (NFM) state to an itinerant metamagnetic state. The NFM state, which occurs in the 0.4 \textgreater\ $x$ \textgreater\ 0.08 range, freezes into a cluster spin glass phase at low temperatures [1]. A quantum phase transition (QPT) occurs as the spin freezing temperature $T_{f}$ is suppressed to zero K near $x=$0.08. In this talk, we will report a novel quantum phase observed near the QPT [2]. The isothermal magnetization $M(H)$ and the temperature dependence of electronic specific heat \textit{Ce}($T )$ of this phaseexhibit anomalous power-law singularities and are controlled by a single exponent. Moreover, the magnetization $M(T,H)$ of this phase is found to follow a phenomenological scaling law of $M(H,T)\propto H^{\alpha}f(H$/$T^{\delta})$. These observations indicate the slow dynamics in rare regions arising from the effect of disorder on the QPT.\\[4pt] [1] Z. Qu et al., Phys. Rev. B 78, 180407(R) (2008)\\[0pt] [2] Z. Qu et al., Phys. Rev. B 86, 014434 (2012).