Influence of grain size and sintering temperature grain size on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.67Sr0.33MnO3 nanoparticles

Highlights: • The effect of grain size and sintering temperature on the critical properties is studied. • The calculated critical exponents are satisfied with the scaling theory. • The β, γ, and δ, found for L6, L8 and L10, are consistent with the Mean-field theory. • For L12, the values of the critical exponents are similar to the (3D) Heisenberg model. • The reduction of grain size strongly influences the universality class. We have undertaken a systematic study of critical behavior in La_0.67Sr_0.33MnO₃ nanoparticles, sintered at different temperatures (L6, L8, L10 and L12 sintered at 600 °C, 800 °C, 1000 °C, 1200 °C respectively), by magnetization measurements. The critical exponents are estimated by various techniques such as the Modified Arrott plot, Kouvel–Fisher plot and critical isotherm technique. Compared to standard models, the critical exponents are close to those expected by the Mean-field model (with β = 0.5 γ = 1, and δ = 3) for (L6, L8, and L10) samples and by the (3D) Heisenberg model (β = 0.365, γ = 1.336 and δ = 4.80) for L12 sample. We conclude that the reduction of grain size strongly influences the universality class.