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.