paper

Magnetic susceptibilities in a family of S=1/2 Kagome antiferromagnet

arXiv:0901.2791 · doi:10.1103/PhysRevB.79.174407

Abstract

Hexagonal antiferromagnets Cs $_{2}$ Cu $_{3}$ MF $_{12}$ (M = Zr, Hf and Sn) have uniform Kagome lattices of Cu $^{2 +}$ with S = 1/2, whereas Rb $_{2}$ Cu $_{3}$ SnF $_{12}$ has a 2a by 2a enlarged cell as compared with the uniform Kagome lattice. The crystal data of Cs $_{2}$ Cu $_{3}$ SnF $_{12}$ synthesized first in the present work are reported. We performed magnetic susceptibility measurements on this family of Kagome antiferromagnet using single crystals. In the Cs $_{2}$ Cu $_{3}$ MF $_{12}$ systems, structural phase transitions were observed at $T_{t} = 225$ K, 172 K and 185 K for M = Zr, Hf and Sn, respectively. The magnetic susceptibilities observed for $T > T_{t}$ are almost perfectly described using theoretical results obtained by exact diagonalization for the 24-site Kagome cluster with $J / k_{B} = 244$ K, 266 K and 240 K, respectively. Magnetic ordering accompanied by the weak ferromagnetic moment occurs at $T_{N} = 23.5$ K, 24.5 K and 20.0 K, respectively. The origins of the weak ferromagnetic moment should be ascribed to the lattice distortion that breaks the hexagonal symmetry of the exchange network for $T < T_{t}$ and the Dzyaloshinsky-Moriya interaction. Rb $_{2}$ Cu $_{3}$ SnF $_{12}$ is magnetically described as a modified Kagome antiferromagnet with four types of neighboring exchange interaction. Neither structural nor magnetic phase transition was observed in Rb $_{2}$ Cu $_{3}$ SnF $_{12}$ . Its magnetic ground state was found to be a spin singlet with a triplet gap. Using exact diagonalization for a 12-site Kagome cluster, we analyzed the magnetic susceptibility and evaluated individual exchange interactions. The causes leading to the different ground states in Cs $_{2}$ Cu $_{3}$ SnF $_{12}$ and Rb $_{2}$ Cu $_{3}$ SnF $_{12}$ are discussed.

12 pages, 9 figures. Submitted to Physical Review B. Errors on Fig. 7 were corrected