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We investigated the crystal structure of Rb$_2$Cu$_3$SnF$_{12}$ and itsmagnetic properties using single crystals. This compound is composed of Kagomelayers of corner-sharing CuF$_{6}$ octahedra with a 2a x 2a enlarged cell ascompared with the proper Kagome layer. Rb$_2$Cu$_3$SnF$_{12}$ is magneticallydescribed as an $S$=1/2 modified Kagome antiferromagnet with four kinds ofneighboring exchange interaction. From magnetic susceptibility and high-fieldmagnetization measurements, it was found that the ground state is a disorderedsinglet with the spin gap, as predicted from a recent theory. Exactdiagonalization for a 12-site Kagome cluster was performed to analyze themagnetic susceptibility, and individual exchange interactions were evaluated.

Singlet Ground State and Spin Gap in S=1/2 Kagome Antiferromagnet Rb$_2$Cu$_3$SnF$_{12}$