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Tuning the phase transition dynamics by variation of cooling field and metastable phase fraction in Al doped Pr$_{0.5}$Ca$_{0.5}$MnO$_3$

We report the effect of field, temperature and thermal history on the time dependence in resistivity and magnetization in the phase separated state of Al doped Pr$_{0.5}$Ca$_{0.5}$MnO$_3$. The rate of time dependence in resistivity is much higher than that of magnetization and it exhibits a different cooling field dependence due to percolation effects. Our analysis show that the time dependence in physical properties depends on the phase transition dynamics which can be effectively tuned by variation of temperature, cooling field and metastable phase fraction. The phase transition dynamics can be broadly divided into the arrested and un-arrested regimes, and in the arrested regime, this dynamics is mainly determined by time taken in the growth of critical nuclei. An increase in cooling field and/or temperature shifts this dynamics from arrested to un-arrested regime, and in this regime, this dynamics is determined by thermodynamically allowed rate of formation of critical nuclei which in turn depends on the cooling field and available metastable phase fraction. At a given temperature, a decrease in metastable phase fraction shifts the crossover from arrested to un-arrested regimes towards lower cooling field. It is rather significant that inspite of the metastable phase fraction calculated from resistivity being somewhat off from that of magnetization, their cooling field dependence exhibits a striking similarity which indicate that the dynamics in arrested and un-arrested regimes are so different that it comes out vividly provided that the measurements are done around percolation threshold.