Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic susceptibilities in a family of S=1/2 Kagome antiferromagnet   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.

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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th