Magnetic phase diagram of (Sr$_{1-x}$Ca$_{x})_{3}$Ru$_{2}$O$_{7 }$ (0$\le $x$\le $1.0)

The layered ruthenates (Sr,Ca)$_{n+1}$Ru$_{n}$O$_{3n+1}$ have received widespread attention in recent years since they display a remarkable range of unique superconducting and magnetic properties, such as spin triplet superconductivity and metamagnetic quantum criticality. We have recently studied properties of the double layered (Sr$_{1-x}$Ca$_{x})_{3}$Ru$_{2}$O$_{7}$ solid solution series and established the magnetic phase diagram of this system using the high-quality single crystals grown by floating-zone method. We have observed rich magnetic ground states in this system: (I) Itinerant metamagnetic state (0.08$>x\ge $0); (II) enhanced PM state accompanied by non-Fermi liquid behaviors near $x\sim $0.08; (III) ferromagnetic cluster glass (CG) phase featuring an extremely large Wilson ratio ($\sim $120) and enhanced electron correlation (0.40$>x>$0.08); (IV) long-range AFM state (1$\ge x\ge $0.40). Furthermore, we found a new phase which shows an unconventional anomalous Hall effect in a low temperature range immediately above the CG phase. The magnetization of this phase is found to follow a new scaling expression derived by phenomenologically extending the quantum Griffiths phase model.