  Using elastic and inelastic neutron scattering techniques with and without
application of an external magnetic field $H$, the magnetic ground states of
Zn$_x$Co$_{4-x}$(OD)$_6$Cl$_2$ ($x=0,1$) were studied. Our results show that
for $x=0$, the ground state is a magnetic long-range ordered (LRO) state where
each tetrahedron forms an "umbrella"-type structure. On the other hand, for
$x=1$, no static ordering was observed down to 1.5 K, which resembles the
behavior found in the isostructural quantum system
Zn$_x$Cu$_{4-x}$(OD)$_6$Cl$_2$. When $H$ field is applied, however the $x=1$
system develops the same LRO state as $x=0$. This indicates that the $x=1$
disordered state is in the vicinity of the $x=0$ ordered state.
