Magnetic Fluctuations in the Hubbard Model on Kagome-based Frustrated Lattices

We report our results on the interplay between electron correlation and magnetic fluctuations in the geometrically-frustrated Kagome and hyper-Kagome Hubbard models at half filling. These models have two different geometrical units important in the low-energy physics: the frustrated triangle and the non-frustrated loop with even-number sites. In order to treat both of them on equal footing, we apply cluster dynamical mean-field theory to large-size clusters up to 12 sites. By calculating the spin susceptibility $\chi({\vec q}, \omega)$, we have found in the Kagome system that an anomalous one-dimensional magnetic correlation previously found near the Mott transition [1] is observed even in the non-interacting case at high temperature, and its temperature range gradually suppressed by increasing electron correlation. This behavior is ascribed to the nesting property at the van-Hove singularity preserved under electron correlation. We will also present the results for hyper-Kagome system in relation to the recent experiments on Na$_4$Ir$_3$O$_8$ [2]. \\ \noindent [1]\ T.\ Ohashi {\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 97}, 066401 (2006)\\ \noindent [2]\ Y.\ Okamoto {\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 99}, 137207 (2007)