Magnetic Susceptibility for $CaV_4O_9$
  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. 
Ken'ichi Takano and Kazuhiro Sano