  Most studies of collective dephasing for bipartite as well as multipartite
quantum systems focus on a very specific orientation of magnetic field, that
is, z-orientation. However, in practical situations, there are always small
fluctuations in stochastic field and it is necessary that more general
orientations of fields should be considered. We extend this problem to
qubit-qutrit systems and study correlation dynamics for entanglement and local
quantum uncertainty for some specific quantum states. We find that certain
quantum states exhibit freezing dynamics both for entanglement and local
quantum uncertainty. We analyze the asymptotic states and find the conditions
for having non-zero entanglement and local quantum uncertainty. Our results are
relevant for ion-trap experiments and can be verified with current experimental
setups.
