Antiferromagnetic metallic state: A transport and thermodynamic study of Ca$_{3}$(Ru$_{1-x}$Cr$_{x}$)$_{2}$O$_{7}$*

Among the variety of exciting physical properties, a signature feature of the bilayered Ca$_{3}$Ru$_{2}$O$_{7}$ is the antiferromagnetic metallic (AFM) state that lies between a Neel temperature, T$_{N}$=56 K and a Mott-like transition (MIT), T$_{MI}$=48 K. The results of our recent thermodynamic and transport study of single crystal Ca$_{3}$(Ru$_{1-x}$Cr$_{x})_{2}$O$_{7}$ (0$\le $x$\le $0.20) reveal that the temperature regime for the AFM state is significantly broadened with T$_{MI }$and T$_{N}$ being pushed to lower and higher temperatures, respectively, as Cr doping (x) increases. In addition, the magnetic easy axis for magnetization moves gradually away from \textbf{\textit{a}}-axis to \textbf{\textit{b}}-axis as x increases and at x=0.20, the magnetic anisotropy in the basal plane diminishes. This reduced spin polarization along the easy axis is promptly reflected in the less pronounced negative magnetoresistance as x increases. Furthermore, the DC current--voltage characteristics show the S-shaped negative differential resistivity for x$\le $0.17. As seen in the pure compound, observed non-ohmic behavior is restricted to the AF nonmetallic region. All results are presented along with comparisons drawn from related systems such as perovskite CaRu$_{1-x}$Cr$_{x}$O$_{3}$ where highly anisotropic magnetism is induced by Cr substitution. * This work was supported by NSF grants DMR-0240813 and DMR-0552267.