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Hirschfeld surface analysis and short-range ferromagnetic ordering in La0.5Ca0.4Ag0.1MnO3 based on critical behavior study

We investigated the Hirschfeld surface analysis and critical behaviour in La0.5Ca0.4Ag0.1MnO3 near the second-order ferromagnetic phase transition at Curie temperature TC. We determined the critical exponents, β, γ and δ corresponding to the temperature dependence of spontaneous magnetization, initial susceptibility and isothermal magnetization, respectively. The study of Hirshfeld surface reflects that both the electrostatic and intermolecular interactions are short range. The values for critical exponents obtained from magnetic measurements are very close to those predicted by the mean field tri-critical model.  The critical-exponent values deduced here were in a good conform to those obtained using the modified Arrott plot and Widom scaling relation.