  We investigate the dynamics of magnetization in the phase separated (PS)
state after introducing the quenched disorder at the Mn-site of a manganite
around half doping. The compound,
Pr$_{0.5}$Sr$_{0.5}$Mn$_{0.925}$Ga$_{0.075}$O$_{3}$, exhibits PS with the
coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) clusters where
the size of the FM clusters is substantially reduced due to the disorder
introduced by nonmagnetic Ga substitution. At low temperature, the system
develops a new magnetic anomaly, which is marked by a peak in the zero field
cooled magnetization. Detailed study of linear as well as nonlinear ac
susceptibilities coupled with dc magnetization indicates that this peak arises
due to the thermal blocking of nanometer size FM clusters demonstrating
superparamagnetic behavior. The system, however, exhibits slow magnetic
relaxation, aging effect, memory effect in both field cooled and zero field
cooled magnetization below the blocking temperature. These imply the presence
of collective behavior induced by the interaction between the clusters.
Moreover, the magnetic relaxation measured with positive and negative
temperature excursions exhibits asymmetric response suggesting that the
dynamics in this phase separated system is accounted by the hierarchical model
rather than the droplet model which are commonly used to describe the similar
collective dynamics in glassy system.
