Universal critical behavior in polycrystalline La_0.75Ca_0.25-xNa_xMnO₃ (x = 0.00; 0.05) samples

Abstract

The critical behavior of the manganese La_0.75Ca_0.25−xNa_xMnO₃ (x = 0.00; 0.05) was studied around the PM-FM phase transition. Various techniques are used to obtain the critical exponents of our samples; such as modified Arrott plot (MAP), Kouvel–Fisher (KF) method and the critical isotherm analysis (CI) around the Curie temperature (Tc). The experimental results indicated that our samples had a second-order magnetic phase transition. Based on the above methods, the critical exponents (β, γ and δ) were extracted in the low- and the high-magnetic fields from the magnetic isotherms data. The obtained critical exponents were close to those expected for the Tricritical Mean-Field model. These critical exponents obey to the Widom scaling relation δ = 1 + γ/β, which proves the reliability and the self-consistency of all critical exponents values. The magnetization–field–temperature (M–µ₀H–T) falls into two curves, below and above T_C. It follows the single scaling equation $M\left( {H,\varepsilon } \right) = \varepsilon^{\beta } f_{ \pm } \left( {\frac{H}{{\varepsilon^{\beta + \gamma } }}} \right)$ with ε = (T–T_C)/T_C is the reduced temperature. This confirms the reasonability of the critical exponents with the scaling hypothesis. Moreover, the analysis of the effective exponents β_eff and γ_eff indicates that β_eff (ɛ) for the two samples and γ_eff (ɛ) for x = 0.00 are self-consistency and in good agreements with the Tricritical mean-Field model, but γ_eff (ɛ) for x = 0.05 is heterogeneous with any class of predicted universality.