Eur. Phys. J. Plus (2021) 136: 23
https://doi.org/10.1140/epjp/s13360-020-00958-9

Regular Article

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

¹ Laboratoire de la Matière Condensée et des Nanosciences, LR11ES40, Département de Physique, Faculté des Sciences de Monastir, Université de Monastir, 5019, Monastir, Tunisia
² Laboratoire des Energies et des Matériaux, LabEM-LR11ES34, Ecole Supérieure des Sciences et de la Technologie, University of Sousse, Road Lamine Abessi, Hammam Sousse, 4011, Sousse, Tunisia
³ Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France

^b maneldhahri1991@gmail.com

Received: 7 August 2020
Accepted: 19 November 2020
Published online: 3 January 2021

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 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.