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Magnetic field-induced instability of the cooperative paramagnetic state in Zn$_x$Co$_{4-x}$(OD)$_6$Cl$_2$

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.