  We have investigated low energy nuclear spin excitations in double perovskite
compounds R$_2$CoMnO$_6$ (R = Y,Tb) by inelastic neutron scattering with a
high-resolution back-scattering spectrometer. We observed inelastic signals at
about 2.1 $\mu$eV for Y$_2$CoMnO$_6$ and also for Tb$_2$CoMnO$_6$ at T = 2 K in
both energy loss and energy gain sides. We interpret these inelastic peaks to
be due to the transitions between the hyperfine split nuclear levels of
$^{59}$Co nucleus. The inelastic peaks move towards the central elastic peak
and finally merge with it at the magnetic ordering temperature $T_C$. The
energy of the low energy excitations decreases continuously and becomes zero at
$T_C \approx 75$ K for Y$_2$CoMnO$_6$ and $T_C \approx 100$ K for
Tb$_2$CoMnO$_6$. For Tb$_2$CoMnO$_6$, which contains magnetic rare-earth ions,
additional quasielastic scattering due presumably to the fluctuations of large
Tb magnetic moments was observed. The present study reveals the magnetic
ordering of the Co sublattice. The results of this investigation along with
that obtained by us for other compounds indicate the presence of unquenched
orbital moments in some of the Co compounds.
