We investigated low energy nuclear spin excitations in the layered compound CoCl$_2$ by high resolution back-scattering neutron spectroscopy. We detected inelastic peaks at $E = 1.34 pm 0.03$ $mu$eV on both energy loss and energy sides of the central elastic peak at $T = 2$ K. The energy of the inelastic peaks decrease with temperature continuously and become zero at $T_N approx 25$ K at which the two ielastic peaks merge with the central elastic peak. We interpret the low energy excitations to be due to the transition between hyperfine field split nuclear levels. The present data together with the data on other Co compounds show that the energy of the nuclear spin excitations of a number of compounds follow a linear relationship with the electronic magnetic moment of the Co ion whereas that of other compounds deviate appreciably from this linear behaviour. We ascribe this anomalous behaviour to the presence of unquenched orbital moments of the Co ions.
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