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We found new two-dimensional (2D) quantum ($S=1/2$) antiferromagnetic systems: $\mathrm{Cu}R{E}_{2}\mathrm{G}{\mathrm{e}}_{2}{\mathrm{O}}_{8}$ ($RE=\mathrm{Y}$ and La). According to our analysis of high-resolution x-ray and neutron diffraction experiments, the Cu network of $\mathrm{Cu}R{E}_{2}\mathrm{G}{\mathrm{e}}_{2}{\mathrm{O}}_{8}$ ($RE=\mathrm{Y}$ and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular $b$ axis. Our bulk characterizations from …