**1. Introduction**

In recent years, magnetic materials exhibiting high magnetocaloric effect (MCE) have been extensively studied experimentally and theoretically because of their intensive necessity in magnetic refrigeration (MR) [1–3]. This recent cooling technology, which is expected to replace traditional expansion/compression gas refrigeration technology, has many particular interests because of its significant economic benefits [4–6]. The magnetic entropy change (ΔSM) is interestingly important for rating the refrigerant properties [7, 8]. Thus, numerous materials exhibiting high MCE have been widely developed in the last decades for exploitation as promising materials in MR technology [9–14].

The mean field model [15, 16] is an efficient tool in the study of magnetic materials [17]. Currently, Amaral et al. have signaled a scaling method based on this model [18].

According to the work of Amaral et al., we have reported, in this paper, our studies on the magnetocaloric properties of the Nd0.67Ba0.33Mn0.98Fe0.02O3 sample which exhibits a second-order ferromagnetic-paramagnetic (FM-PM) phase transition [19], by scaling the experimental magnetization. We have showed, in this work, how the mean field theory may adequately model the magnetic and the magnetocaloric properties of this magnetic system, which may be applicant in MR technology.

The scaling method based on the mean field model leads us to estimate directly the saturation magnetization Mð Þ<sup>0</sup> , the exchange parameter ð Þλ , the total angular momentum Jð Þ, and the Lande factor gð Þ of our sample. These parameters are necessary for simulating magnetization isotherms, M Hð Þ *;* T , which are used for the calculation of the magnetic entropy change (�ΔSM) of Nd0.67Ba0.33Mn0.98Fe0.02O3 material. In addition, the second-order phase transition FM-PM of this sample is confirmed by analyzing the Bean-Rodbell model [20, 21].

**Figure 2** shows the variation of the magnetization as a function of the varied magnetic field up to 10 T, at very low temperature (10 K), for the undoped compound Nd0.67Ba0.33MnO3 and for the doped compound Nd0.67Ba0.33Mn0.98Fe0.02O3. It is apparent in this figure that in spite of the intense magnetic applied field (10 T), the magnetization does not attain saturation. This is due to the presence of

*Modeling the Magnetocaloric Effect of Nd0.67Ba0.33Mn0.98 Fe0.02O3 by the Mean Field Theory*

orbital. Effectively, a comparison between magnetization of the two compounds Nd0.67Ba0.33MnO3 [19] and La0.67Ba0.33MnO3 [22] are depicted in **Figure 3**. This figure shows obviously that the lanthanum compound rapidly reaches saturation even under low applied magnetic field. This is because of the non-contribution of the La3+ ion ( Xe ½ �Þ in magnetism which has no electrons in 4f orbital. **Figure 2** also indicates that a 2% iron doping proportion in Nd0.67Ba0.33Mn0.98Fe0.02O3 decreases the magnetization by 0.12μ<sup>B</sup> (3.94 μ<sup>B</sup> for Nd0.67Ba0.33MnO3, whereas Nd0.67Ba0.33Mn0.98Fe0.02O3 presents 3.82 μB) under a 10 T applied magnetic field of, in a good agreement with an antiferromagnetic coupling between Mn<sup>3</sup><sup>þ</sup> and Fe3<sup>þ</sup> spin sub-lattices as demonstrated by the Mössbauer spectroscopy studies [23, 24]. As knowing, the orbital momentum is quenched by the crystal field in the octahedral site

of manganite for transition elements, so only the spin of Fe3<sup>þ</sup> ([Ar]3d5

*Comparison of* M *versus* H *at* T ¼ 10 K *for Nd0.67Ba0.33MnO3 and Nd0.67Ba0.33Mn0.98Fe0.02O3 samples.*

*Comparison of* M *versus* H *at* T ¼ 10 K *La0.67Ba0.33MnO3 and Nd0.67Ba0.33MnO3 for samples.*

Þ which have three electrons in the 4f

) contributes to

the magnetic moments of Nd<sup>3</sup><sup>þ</sup>( Xe ½ � 4f <sup>3</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.82559*

**Figure 2.**

**Figure 3.**

**13**
