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Spin-spin relaxation time ($T_2$) and magnetic susceptibility ($chi$) of the second layer $^3$He adsorbed on Grafoil, exfoliated graphite, preplated with a monolayer $^4$He are studied by pulsed-NMR in a density range of $0.68 leq rho leq 5.28$ nm$^{-2}$. The temperature dependence of $chi(T)$ and $chi(T = 0)$ show Fermi fluid behaviour and no evidence of self-condensation are found even at the lowest density $rho = 0.68$ nm$^{-2}$. Density dependence of $T_2$ at $f = 5.5$ MHz shows a broad maximum of 5.7 ms around $rho = 3$ nm$^{-2}$. Since the decrease of $T_2$ in dilute side can not be expected in the ideal 2D fluid, it can be understood as the relaxation caused by a small amount of solid $^3$He at heterogeneity of the substrate. We also measured the Larmor frequency dependence of $T_2$ at $rho = 5.28$ nm$^{-2}$. $1/T_2$ has a $f$-linear dependence similarly to the earlier study on a first layer solid $^3$He. From a comparison between our result and the earlier one, this linearity is almost independent of the particle motion. Now, it could be caused by a microscopic magnetic field inhomogeneity arisen from the mosaic angle spread and diamagnetism of the graphite substrate.
Using an exact diagonalization technique on small clusters, we study spin and density excitations of the triangular-lattice $t$-$J$ model with multiple-spin exchange interactions, whereby we consider anomalous properties observed in the doped Mott re
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