Study of the Critical Behavior in La0.67Ca0.18Sr0.15Mn0.98Ni0.02O3 Manganite Oxide

*Kawther Laajimi, Mohamed Hichem Gazzah and Jemai Dhahri*

## **Abstract**

In order to study the critical behavior of La0.67Ca0.18Sr0.15Mn0.98Ni0.02O3 near room temperature, magnetization measurements were performed. It can be seen from the findings that the specimens show a second order phase transition. Given the relative slope, the 3D-Ising model was deduced as the most suitable model. It was found that the evaluated critical exponents were *β* ¼ 0.320, *γ* ¼ 1.296 and *δ* ¼ 4.965 at *T*<sup>C</sup> ¼ 319 K. These verify the Broadom's scaling equation *δ* ¼ 1 þ *γ*/*β*, which demonstrates that our values have been proved valid. Near *T*<sup>C</sup> magnetizationstrength-temperature, (*M-μ*0*H*-*T*) results fell in two curves according to critical exponents, obeying the single scaling equation *<sup>M</sup>*ð Þ¼ *<sup>μ</sup>*0*H*, *<sup>ε</sup> <sup>ε</sup>β<sup>ʄ</sup>* � *<sup>μ</sup>*0*H=εβ*þ*<sup>γ</sup>* with *ε* ¼ ð Þ *T* � *T*<sup>c</sup> *=T*<sup>c</sup> as the reduced temperature.

**Keywords:** magnetic materials, critical behavior, spontaneous magnetization, 3D Ising model, Kouvel-Fisher method

### **1. Introduction**

Extensive research on Ln1 � *<sup>x</sup>*A*<sup>x</sup>* MnO3 (Ln ¼ La; A ¼ Ca, Sr, Ba, Pb, etc.) holedoped manganite has attracted significant attention, for its specific transport and magnetic properties and its potential for being used over the years for future technological purposes, which are based on the colossal magnetoresistance effect (CMR) [1, 2] and magnetocaloric behavior [3, 4]. For a more detailed understanding of the relationship that exists between the insulator-to-metal transition and the CMR effect, it is necessary to answer two fundamental issues concerning the ferromagnetic (FM) paramagnetic (PM) phase transition temperature: firstly, the order of the phase transition and, secondly, the common universality class. The detailed study of the critical exponents around the FM-PM transition is essential to address this point [5, 6]. In this way, it can be considered that this transition can be explained through the double exchange phenomenon (DE), and by the percolation process, phase separation [7], electron–phonon pairing [8], the effect of quenched disorder [9] and the observation of the Griffiths phase (GP) [9]. Initially, on the DE model, the description of the critical behavior relied on a long-range mean field theory [10, 11]. Later, the work of Motome-Furulawa [12, 13] which suggested a short-range Heisenberg model for

critical behavior comprising only nearest-neighbor exchange, was carried out by taking into account the existence of a short-range interaction at the level of localized spins. In addition, various pertinent experimental studies on critical phenomena confirm that view also the resulting critical exponent data. In accordance with the one obtained by conventional ferromagnetic Heisenberg model. Taking the data from the DC magnetic study, researchers Ghosh et al. [14] have pointed out that critical exponent *β* is found to be 0.37 at *La*0*:*7*Sr*0*:*3*MnO*<sup>3</sup> ferromagnetic manganite. (*β* = 0.365 for the Heisenberg model, in which case the critical exponent *β* was in close contact to the temperature dependency over the spontaneous magnetization under the Curie temperature *T*C) as well as the critical case value of *β* = 0.374 has been also referred in the ferromagnet DE *Nd*0*:*6*Pb*0*:*4*MnO*<sup>3</sup> [15]. Nevertheless, a rather elevated value that was *β* = 0.5 achieved in La0.8Sr0.2 MnO3 polycrystals was consistent to the one found in the mean field pattern [16]. In contrast, the small value of the critical exponent in terms of *β* = 0.14 that was found in La0.7Ca0.3MnO3 monocrystal indicates a first-order rather than second-order PM-FM transition occurring in this system [17]. Between, there was finding of moderate critical value of *β* = 0.25 in the polycrystalline *La*0*:*6*Ca*0*:*4*MnO*<sup>3</sup> was in a fair agreement with the values of the tricritical point [18, 19]. Thus, various critical exponents have been seen *β* ranging between 0.1 and 0.5, now, there are four different types of theoretical patterns, mean-field model (*β* = 0.5), three-dimensional (3D) Heisenberg (*β* = 0.365), 3D-Ising (*β* = 0.325), as well as tricritical mean-field (*β* = 0.25), which have been employed in order to have some explanation of the critical characteristics provided by manganites. Given the discrepancy between the reported critical values, it is necessary to examine the critical behavior of similar manganite perovskites.

In this chapter, we concentrate on a more detailed evaluation of the critical exponents α, *β* and *γ* as well as the Curie temperature *T*<sup>C</sup> for La0.67Ca0.18Sr0.15Mn0.98Ni0.02O3 compound near the FM-PM phase transition temperature by carrying out analyses using different techniques.
