  We measure the cosmological bias factor of DLAs from their cross-correlation
with the Ly$\alpha$ forest absorption, as a function of the DLA metal strength,
defined from an average of equivalent widths of the strongest detectable
low-ionization metal lines. A clear increase of the bias factor with metal
strength is detected, as expected from a relation of metallicity and velocity
dispersion with host halo mass. The relation is stronger after the metal
strength is corrected for the HI column density, to make it more related to
metallicity instead of metal column density. After correcting for the effects
of measurement errors of the metal strength parameter, we find that the bias
factor of DLAs with the weakest metal lines is close to unity, consistent with
an origin in dwarf galaxies with host halo masses $\sim10^{10} M_{\odot}$,
whereas the most metal rich DLAs have a bias factor as large as $b_{\rm DLA}
\sim 3$, indicative of massive galaxies or galaxy groups in host halos with
masses $\sim 10^{12} M_{\odot}$. Our result confirms the physical origin of the
relation of bias factors measured from cross-correlation studies to the host
halos of the absorbers.
