Critical behavior and the universal curve for magnetocaloric effect in Pr 0.6 Ca 0.1 Sr 0.3 Mn 1x Fe x O 3 (x = 0, 0.05 and 0.075) manganites Saoussen Mahjoub a,⇑ , Mohamed Baazaoui a , Rafik M’nassri a,b , Nassira Chniba Boudjada c , Mohamed Oumezzine a a Laboratoire de Physico-Chimie de s Matériaux, Département de Physique, Faculté des Sciences de Monastir, Université de Monastir, 5019 Monastir, Tunisia b Higher Institute of Applied Sciences and Technology of Kasserine, Kairouan University, BP 471, 1200 Kasserine, Tunisia c Institut NEEL, B.P. 166, 38042 Grenoble Cedex 9, France article info Article history: Received 1 November 2014 Received in revised form 1 February 2015 Accepted 2 February 2015 Available online 11 February 2015 Keywords: Manganites Critical exponents Magnetization Master curve abstract We have investigated the critical behavior of the ferromagnetic Pr 0.6 Ca 0.1 Sr 0.3 Mn 1x Fe x O 3 (x = 0, 0.05 and 0.075) compounds by the data of magnetization measurements. To investigate the nature of the magnetic phase transition, a detailed critical exponent study has been performed. The critical exponents b, c, and d determined using the modified Arrott plot (MAP), the Kouvel–Fisher method (KF), as well as the critical isotherm (CI) analysis. With these critical exponents, the experimental M (T, H) relations below and above Curie temperature collapse into two universal branches, fulfilling the single scaling equation m = f±(h), where m and h are renormalized magnetization and field respectively. The estimated critical exponents b (0.361 6 b 6 0.380), c (1.254 6 c 6 1.342) and d (4.30 6 d 6 4.71) are close to those expected for three- dimensional Heisenberg. Interestingly, for the doped samples the values of c decreased and approached the 3D-Ising (c = 1.24). This reflects an existence of ferromagnetic short-range order in our samples. The substitution of Mn by Fe greatly weakens the influence of double exchange (DE) interactions and promotes the antiferromagnetic interactions (AFM). Moreover, the temperature dependence of the expo- nent n for a different magnetic field is also studied. The values of n obey to the Curie Weiss law above the transition temperature. In particular, n can be related to the critical exponents b, c and d at the magnetic transition from the relation nðT C Þ¼ b1 bþc   þ 1 ¼ 1 þ 1 d 1  1 b   ; where n = 0.624, 0.617 and 0.620. These results confirmed the invalidity of mean field theory. Moreover, rescaled entropy data for all composi- tions collapses into the same universal curve, revealing universal behavior for the magnetocaloric effect in this series of compounds. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction The strongly correlated manganites with perovskite structure A 1x B x MnO 3 (A = rare-earth ions; B = divalent ions) have a strong coupling between the spin, charge, orbital, and lattice degree of freedom which lead to a series of novel behaviors related to basic concepts and important questions in modern physics and material science [1,2]. Many theories such as double-exchange (DE) interac- tions taking place between Mn 3+ and Mn 4+ ions [3–5], polaronic effects and phase separation have been proposed to understand the underlying physics of the manganites [6]. Shortly, these mate- rials have also been found to exhibit the large magnetocaloric effect (MCE) under a moderate applied field revealing that the colossal magnetoresistance (CMR) manganites are possible candidates for magnetic refrigeration applications [7–9]. One approach to understand the complex phase transition phenomena in manganites undergoing a second order magnetic phase transi- tion is to study the critical exponents interrelated with the mag- netic transition. Manganites are intrinsically inhomogeneous, both above and below paramagnetic (PM)–ferromagnetic (FM) transition temperature (T C ). So, critical exponents for manganites show large variations which cover almost all the universality class- es even for the similar system when several experimental tools are used to determine them [10,11]. Such critical exponents give an idea about the nature and type of magnetic interaction and the in-depth knowledge of magnetic phase transition. Moreover, the study of critical phenomena in the DE ferromag- netic system is of interest, since the magnetic interaction is propor- tional to cos h/2 (h is the angle between the directions of ionic http://dx.doi.org/10.1016/j.jallcom.2015.02.011 0925-8388/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: mahjoub.sawssen@gmail.com (S. Mahjoub). Journal of Alloys and Compounds 633 (2015) 207–215 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom