Hole-doping dependence of percolative phase separation in Pr_(0.5-delta)Ca_(0.2+delta)Sr_(0.3)MnO_(3) around half doping

We address the problem of the percolative phase separation in polycrystalline samples of Pr$_{0.5-\delta}$Ca$_{0.2+\delta}$Sr$_{0.3}$MnO$_3$ for $-0.04\leq \delta \leq 0.04$ (hole doping $n$ between 0.46 and 0.54). We perform measurements of X-ray diffraction, dc magnetization, ESR, and electrical resistivity. These samples show at $T_C$ a paramagnetic (PM) to ferromagnetic (FM) transition, however, we found that for $n>0.50$ there is a coexistence of both of these phases below $T_C$. On lowering $T$ below the charge-ordering (CO) temperature $T_{CO}$ all the samples exhibit a coexistence between the FM metallic and CO (antiferromagnetic) phases. In the whole $T$ range the FM phase fraction ($X$) decreases with increasing $n$. Furthermore, we show that only for $n\leq 0.50$ the metallic fraction is above the critical percolation threshold $X_C\simeq 15.5%$. As a consequence, these samples show very different magnetoresistance properties. In addition, for $n\leq 0.50$ we observe a percolative metal-insulator transition at $T_{MI}$, and for $T_{MI}<T<T_{CO}$ the insulating-like behavior generated by the enlargement of $X$ with increasing $T$ is well described by the percolation law $\rho ^{-1}=\sigma \sim (X-X_C)^t$, where $t$ is a critical exponent. On the basis of the values obtained for this exponent we discuss different possible percolation mechanisms, and suggest that a more deep understanding of geometric and dimensionality effects is needed in phase separated manganites. We present a complete $T$ vs $n$ phase diagram showing the magnetic and electric properties of the studied compound around half doping.