  A detailed study of the low-temperature magnetic state and the relaxation in
the phase-separated colossal magnetoresistance Nd2/3Ca1/3MnO3 perovskite has
been carried out. Clear experimental evidence of the cluster-glass magnetic
behavior of this compound has been revealed. Well defined maxima in the
in-phase linear ac susceptibility $\chi ^{/}(T)$ were observed, indicative of
the magnetic glass transition at $T_{g}$ = 60 K. Strongly divergent
zero-field-cooled and field-cooled static magnetizations and frequency
dependent ac susceptibility are evident of the glassy-like magnetic state of
the compound at low temperatures. The frequency dependence of the cusp
temperature Tmax of the $\chi ^{/}(T)$ susceptibility was found to follow the
critical slowing down mechanism. The Cole-Cole analysis of the dynamic
susceptibility at low temperature has shown extremely broad distribution of
relaxation times, indicating that spins are frozen at "macroscopic" time scale.
Slow relaxation in the zero-field-cooled magnetization has been experimentally
revealed. The obtained results do not agree with a canonical spin-glass state
and indicate a cluster glass magnetic state of the compound below $T_{g}$,
associated with its antiferromagnetic-ferromagnetic nano-phase segregated
state. It was found that the relaxation mechanisms below the cluster glass
freezing temperature $T_{g}$ and above it are strongly different. Magnetic
field up to about $\mu_{0}$H = 0.4 T suppresses the glassy magnetic state of
the compound.
