Relation between structure and magnetic properties in (Sr$_{1-x}$Ca$_{x})_{3}$Ru$_{2}$O$_{7}$

The (Sr$_{1-x}$Ca$_{x})_{3}$Ru$_{2}$O$_{7}$ solid solution series exhibits rich magnetic ground states, ranging from itinerant metamagnetism, ferromagnetic instability, ferromagnetic cluster glass, to antiferromagnet.$\left[1\right]$ In this talk, we report a study on the relation between structure and magnetic properties in (Sr$_{1-x}$Ca$_{x})_{3}$Ru$_{2}$O$_{7}$. Our Rietveld refinement of x-ray scattering data shows that the rotation angle of RuO$_{6}$ octahedra increases with increasing $x$, and approaches saturation for $x>$0.2. The orthorhombicity, which is caused by the tilting of RuO$_{6}$ octahedra, occurs for $x>$0.4 and enhances significantly for $x>$0.7. By comparing these structural characteristics with the magnetic properties, we conclude that the ferromagnetic instability originates from the RuO$_{6}$ octahedra rotation, and the tilting of RuO$_{6}$ octahedra causes a significant magnetic anisotropy.\\ $\left[1\right]$ Z. Qu \textit{et al.} arXiv:0708.1291 (2007).