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

Abstract

We investigate the effect of lightly Pr3+ doping ions on the critical behavior of (La1-xPrx)0.67Ba0.33MnO3 (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, TC. 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)0.67Ba0.33MnO3 (x = 0.15–0.22), with β = 0.55–0.49, γ = 1.06–1.01, and δ = 2.702–3.299. These values indicate that the magnetic order due to lightly Pr3+ 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) ~ r4.56 and ~ r4.49 for 15-at. % Pr and 22-at., respectively. We argue that the range of interaction extends beyond the nearest neighbors.