Hole-doping dependence of percolative phase separation in Pr_0.5-δCa_0.2+δSr_0.3 MnO₃ around half doping

We address the problem of the percolative phase separation in polycrystalline samples of Pr_0.5-δCa_0.2+δSr_0.3 MnO₃ for -0.04≤δ≤0.04 (hole doping n between 0.46 and 0.54). We perform measurements of x-ray diffraction, dc magnetization, electron spin resonance (ESR), and electrical resistivity. These samples show a paramagnetic (PM) to ferromagnetic (FM) transition at the Curie temperature T_C. However, for n>0.50 we found that in a wide temperature range below T_C an important PM volume still survives, coexisting with the FM phase. On lowering T below the charge-ordering (CO) temperature T_CO all the samples exhibit a coexistence of 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≤0.50 the metallic fraction is above the critical percolation threshold Xc≃15.5%. As a consequence, these samples show very different magnetoresistance properties. In addition, for n≤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 p^-1=δ∼(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.