Critical behavior near the ferromagnetic to paramagnetic phase transition temperature in polycrystalline La0.5Sm0.1Sr0.4Mn1−xInxO3 (0≤x≤0.1)

•Sol–gel technique is low cost, simple and easy to handle.•The β, γ and δ critical exponents are determined with various techniques.•We deduce from (RS) that the 3D Ising model is the most adequate model.•The obtained critical exponents fulfill Widom scaling relation. In this paper we report on the critical analysis of the La0.5Sm0.1Sr0.4Mn1−xInxO3(0⩽x⩽0.1) manganites near the ferromagnetic-paramagnatic phase transition temperature. Various techniques such as modified Arrott plot, Kouvel–Fisher method and critical isotherm were used to analyze the magnetic-field dependence of magnetization. The Curie temperature (TC) could be tuned over a wide temperature range, from 251K to 310K, with varying in content. Though the nature of this transition is found to be of second order, the estimated critical exponents β, γ, and δ obtained for different values of x are close to the theoretically predicted values for the three-dimensional (3D)-Ising interaction model (β=0.324±0.01, γ=1.240±0.13 at TC=310K for x=0.00); (β=0.329±0.04, γ=1.241±0.001 at TC=294K for x=0.05); (β=0.332±0.01, γ=1.250±0.04 at TC=251K for x=0.10) and are very far away from any other known universality class. The critical isotherm M (TC, µ0H) gives δ=5.02±0.01 for x=0.00. Thus, the scaling law δ=1+γ/β is fulfilled. The critical exponents obey the single scaling equation of M(μ0H,ε)=εβf±(μ0H/εβ+γ); where f+ for T>TC and f− for T