Critical Exponent Analysis and Evidence of Long-Range Ferromagnetic Order in Lightly Pr-Doped Nanocrystalline (La1-xPrx)0.67Ba0.33MnO3 (x=0.15 and 0.22) Manganites

We investigate the effect of lightly Pr(3+)doping ions on the critical behavior of (La1-xPrx)(0.67)Ba0.33MnO3(x = 0.15-0.22) perovskite synthesized by the modified sol-gel Pechini method. The obtained critical exponents (beta, gamma and delta) have been investigated by measuring the magnetization around the Curie temperature,T-C. Based on the modified Arrott plot and Kouvel-Fisher techniques, scaling hypothesis, and critical isotherm analysis, we have determined the critical exponent values characteristic of magnetic order of (La1-xPrx)(0.67)Ba0.33MnO3(x = 0.15-0.22), with beta = 0.55-0.49,gamma = 1.06-1.01, and delta = 2.702-3.299. These values indicate that the magnetic order due to lightly Pr(3+)doping exhibits long-range ferromagnetic ordering. This fact is in good agreement with the mean-field model. In addition, the exchange interaction is obtained as J(r) similar to r(4.56)and similar to r(4.49)for 15-at. % Pr and 22-at., respectively. We argue that the range of interaction extends beyond the nearest neighbors.