Antiferromagnetism and geometrical frustration in one-dimensional Ca$_{5}$Ir$_{3}$O$_{12}$ and Ca$_{4}$IrO$_{6}$ single crystals*

We report a structural, thermodynamic and transport study of the newly synthesized single crystal Ca$_{5}$Ir$_{3}$O$_{12}$ and Ca$_{4}$IrO$_{6}$. Both materials consist of a triangular lattice of spin chains running along the c-axis. Ca$_{5}$Ir$_{3}$O$_{12 }$and Ca$_{4}$IrO$_{6}$ are antiferromagnetically ordered below 7.8 K and 12 K, respectively. The study reveals an unusually large ratio of the Curie-Weiss temperature to the Neel temperature ($>$36 for Ca$_{5}$Ir$_{3}$O$_{12})$ and a small entropy removal associated with the magnetic phase transition. In addition, the magnetic susceptibility and heat capacity show that the phase transition is essentially insensitive to the application of the magnetic field. All results suggest the presence of the geometrical frustration that causes incomplete long-range antiferromagnetic order. The results will be presented and discussed along with comparisons drawn with other related systems.