Spin Gap in Two-Dimensional Heisenberg Model for CaV4_4O9_9

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.Comment: 8 pages, 6 figures available upon request (Revtex

Magnetic Susceptibility for CaV4O9CaV_4O_9

We examine experimental magnetic susceptibility $\chi^{tot}(T)$ for CaV$_4$O$_9$ by fitting with fitting function $\alpha \chi^{mag}(T) + c$. The function $\chi^{mag}(T)$ is a power series of 1/T and the lowest order term is fixed as $C/T$, where $C$ is the Curie constant as determined by the experimental $g$-value (g=1.96). Fitting parameters are $\alpha$, $c$ and expansion coefficients except for the first one in $\chi^{mag}(T)$. We determine $\alpha$ and $c$ as $\alpha \simeq$ 0.73 and $c\simeq$ 0 for an experimental sample. We interpret $\alpha$ as the volume fraction of CaV$_4$O$_9$ in the sample and $\chi^{mag}(T)$ as the susceptibility for the pure CaV$_4$O$_9$. The result of $\alpha \ne 1$ means that the sample includes nonmagnetic components. This interpretation consists with the result of a perturbation theory and a neutron scattering experiment.Comment: 4pages, 4figure