Inﬂuence of Non-magnetic Ti 4 + Ion Doping at Mn Site on Structural, Magnetic, and Magnetocaloric Properties of La 0 . 5 Pr 0 . 2 Sr 0 . 3 Mn 1 − x Ti x O 3 Manganites (x = 0.0 and 0.1)

Polycrystalline perovskite AMn 1 − x TiO 3 with A = La 0.5 Pr 0.2 Sr 0.3 ( x = 0.0 and 0.1) have been prepared using solid-state reaction method. X-ray powder diffraction and Rietveld refinement revealed that all samples crystallize in a rhombohedral structure with space group R ¯ 3c From M–T curve, we determined the Curie temperature, where the magnetization value decreases abruptly. The Curie temperature ( T C ) decreases from 280 to 123 K when the percentage of Ti increases to 10%. The values of the magnetization M(H) decrease when increasing the Ti content. Moreover, the magnetocaloric effect (MCE) was estimated in terms of isothermal entropy change ( − (cid:2)S M ) using the M (T, μ 0 H) data and employing the thermodynamic Maxwell equation. In addition, using a phenomenological model, we determine magnetocaloric effect from the calculation of magnetization as a function of temperature under different external magnetic fields. Also, we can determine the relative cooling power (RCP) and the specific heat which varies from 2.803 to 7.354 J/(kg/K) for the undoped sample from M(T , μ 0 H) data at different magnetic fields theoretically.


Introduction
Manganites are compounds which have a great effect on technological development because they are widely used in magnetic refrigeration and in magnetic recording [1][2][3]. A Manganites of type Ln 1−x A x MnO 3 , where Ln is a rareearth cation such us La, Pr, Nd, etc. and A is an alkali or alkaline earth cation such as Ca 2+ , Sr 2+ , Ba 2+ , Na 2+ , Pb 2+ , etc. [4,5] are characterized by a mixed valence because of the coexistence of Mn 3+ and Mn 4+ in the B site. These ions are responsible of the magnetic properties due to the double exchange theory that has been suggested by Zener [6]. Samples could be ferromagnetic-metallic, paramagnetic-insulating, ferromagnetic-insulating, or spin glass. These characteristics depend on the ratio Mn 3+ /Mn 4+ which is affected by the substitution in the B site [7][8][9][10][11][12][13][14]. In this research paper, we substitute the Mn by Ti in the mother compound of La 0.5 Pr 0.2 Sr 0.3 MnO 3 . The choice of Ti is made for two major reasons. Firstly, Ti exists in a state of valence 4+ in the structure of perovskite. So, this will affect the mixed valence between Mn 3+ and Mn 4+ resulting in the double exchange (DE) interaction between Mn 3+ and Mn 4+ . Secondly, Ti 4+ is a non-magnetic ion. Therefore, influence of substitution ions 4+ such as Sn 4+ and Ti 4+ for Mn in manganites has been studied [15][16][17]. However, there is some evidence for its influence on magnetocaloric effect. This study is expected to provide data to clarify this issue.

Experimental
Samples La 0.5 Pr 0.2 Sr 0.3 Mn 1−x TiO 3 with x = 0.0 and 0.1 were prepared using a solid-state reaction of La 2 O 3 , SrCO 3 , Pr 6 O 11 , Mn 2 O 3 , and TiO 2 as precursors, all with purity of more than 99.9%. The mixture was first heated in air at 700 • C for 1 day; it is the chamottage to realize decarbonation and to eliminate all organic phases. After that, grinding will take place, and then they were reheated at 1200 • C for 24 h and reground to ensure homogenization. Then, the powder was pressed into pellet forms under 4 tonnes/cm 2 and sintered at 1250 • C for 1 day. The cycle of grinding sintering and pelleting is repeated several times in order to eliminate all parasitic phase. Finally, in order to determine the mesh parameters and the magnetic properties of our samples, we pass them through an X-ray diffraction (XRD) analysis (Cu-K α radiation λ Cu = 1.5406Å); the X-ray diffraction measurements were conducted at the Department of Physics in the University of Coimbra, Portugal. Magnetization vs. temperature was carried out using BS2 magnetometer developed in Louis Neel Laboratory of Grenoble.

Structural Characterization
In order to test the purity of our compounds, we pass them on a powder X-ray diffractometer, and the diffraction spectra obtained for our samples La 0.5 Pr 0.2 Sr 0.3 Mn 1−x TiO 3 (x = 0.0 and 0.1) are shown in Fig. 1. The analysis of these spectra shows that they are a single phase. This is a rhombohedral system associated with the R3c space group. It is noted that for some peaks, there is a shift toward the small 2θ for the titanium-doped sample compared with the parent compound La 0.5 Pr 0.2 Sr 0.3 MnO 3 . This shift corresponds to an increase in the mesh parameters of the La 3+ Pr 3+ Sr 2+ (0.7Mn 3+ (0.3-x) Mn 4+ xTi 4+ O 2− 3 sample. This evolution makes it possible to think that the Ti 4+ ions are well intercalated on the sites of the Mn 4+ ions which is confirmed not only by the increase of cell parameters but also by the increase of the volume of the mesh. For this reason, the intercalation of titanium instead of Mn 4+ cause the increase of the volume which varies from 347.71Å 3 for x = 0.0 to 347.85Å 3 for x = 0.1. Indeed, forx = 0.0, we have in the B site 70% Mn 3+ and 30% Mn 4+ whereas for x = 0.1, we have 70% Mn 3+ , 20% Mn 4+ , and 10% Ti 4+ , and this has no influence on the rate of oxygen.  Table 1 Refined profile parameters for La 0.5 Pr 0.2 Sr 0.3 Mn 1−x Ti x O 3 (x = 0.0 and 0.1) after the Rietveld refinements of X-ray powder diffraction at room temperature (300 K)  Figure 2 discloses the X-ray powder diffraction pattern with the fitted curve forx = 0.0. The refined parameters found using the standard Rietveld process which is based on the use of the FULLPROF program are regrouped in Table 1. The quality of the refinement is estimated via the goodness-of-fit indicator χ 2 .

Magnetic Characterization
All samples AMn 1−x TiO 3 (x = 0.0 and 0.1) present only one transition from the ferromagnetic (FM) to paramagnetic (PM) when the temperature increases (Fig. 3). This confirms the good crystallization of the samples. The Curie temperature is determined using the dM/dT curve; T C is the extremum from this curve and decreases from 280 K for x = 0.0 to 123 K for x = 0.1. The evolution of the Curie temperature can be explained not only by the decrease of the number of Mn 3+ -O 2− -Mn 4+ and consequently increase of the number of Ti 4+ -O 2− -Ti 4+ chains but also by the effect of the cation size in the Mn site. We conclude that the introduction of titanium Ti 4+ causes a significant decrease of the ferromagnetic ordering temperature of the undoped system. In the sample doped by titanium (x = 0.1), we note that the FM-PM transition spreads on an important temperature range (no stiff transition). It shows that the natural magnetic order for this sample is difficult to identify with magnetization (M) vs. temperature (T ) data. Therefore, it is necessary to conduct zero-field-cooled (ZFC) and fieldcooled (FC) measurements.
We can observe the existence of a difference between ZFC M (T ) and FC M (T ) curves in Fig. 3 for x = 0.1, indicating a thermomagnetic irreversibility. In addition, the ZFC curve for the sample doped with 10% titanium (x = 0.1) shows a clear cusp at low temperature (32 K), which is generally thanks to a spin-glass or a cluster-glass state. The irreversibility temperature (T irr ) of zero-field-cooled and field-cooled curves varies from 200 K for x = 0.0 to 106 K for x = 0.1; also, this irreversibility between ZFC M (T ) and FC M (T ) curves only illustrates the T <T C , the domination of the magnetic anisotropy [18]. This anisotropy comes from a spin-orbit coupling and results in the blocking of magnetic moments by the crystalline field [19]. Therefore, to each ferromagnetic material, we define a direction of easy magnetization which depends on the crystal symmetry (cubic, orthorhombic, rhombohedral, etc.). The energy, associated with the magneto-crystalline anisotropy, is a function of the anisotropy constants (K 1 , K 2 , etc.). These constants depend on the materials and the turnaround time of the thermally activated magnetization which is given by the Arrhenius law [20].
where • τ 0 is the attempt time of the order of (10 9 -10 13 ); • E a is the anisotropy energy barrier for small applied defined as: E a = KV; [21], T B (T irr ) is the blocking temperature, and K B is the Boltzman constant; • V is the volume of a single particle; • K is the anisotropy constant.
In this paragraph, we are interested in studying the magnetocaloric effect of La 0.5 Pr 0.2 Sr 0.3 Mn 1−x TiO 3 (x = 0.0 and 0.1). The MCE is intrinsic to magnetic materials and is induced via coupling of the magnetic sublattice with the magnetic field, which alters the magnetic part of the total entropy due to a corresponding change of the magnetic field. The total entropy of a magnetic solid is the total of the lattice, electronic, and magnetic entropy (S L , S E , and S M , respectively). The MCE can be estimated via the magnetic entropy change (− S M ). In addition, the MCE has a significant technological importance since magnetic materials with large values of (− S M ) can be employed in various thermal devices.   [22].
The magnetic entropy is related to the M, μ 0 H , and absolute T through the Maxwell relation [23,24]: where ∂S ∂μ 0 H T is the experimental value obtained from M(μ 0 T ) curves under μ 0 H . One can use the following expression: The (− S M ) variation was obtained by using a program carried out in our laboratory by Pr. N. Fourati and E. Dhahri and by standing on (3). We have traced the variation of the magnetic entropy changes as a function of temperature at different magnetic fields. The spin lattice coupling in the magnetic ordering process is the reason behind this large magnetic entropy change in manganites.

Theoretical Considerations
Applying the phenomenological model [25], the variation of the magnetization as a function of temperature and T C is given by: where M i defines the initial value of magnetization and M f presents the final value of magnetization at the FM-PM transition as ploted in Fig. 6. Here, B and S C are respectively the magnetization sensitivity dM dT at ferromagnetic state before transition, and the magnetization sensitivity dM dT at T C Fig. 6 Temperature dependence of magnetization in constant applied magnetic field A magnetic entropy change of a magnetic system under adiabatic magnetic-field variation from 0 to final value H max is available by S M attains the maximum at T = T C , and its value can be calculated using the following equation:   [26] which is a useful parameter that provides a measure of the effectiveness of magnetic materials for applications in MR.
The δT FWHM is determined by: The RCP is defined as The value of the specific heat is given by [27]: According to this model [25], the specific heat can be rewritten as follows:

Simulation
In order to apply the proposed phenomenological model showing modeled data using model parameters given in Table 2 for x = 0.0 and Table 3 for x = 0.1 it is important to mention that there is a good concordance between the experimental and the calculated results. The M(T ) curves demonstrate that all samples present a magnetic transition from the FM state to the PM one (1 ≤ μ 0 H ≤ 5) when the temperature increases which is shown in Fig. 7a (x = 0.00, b (x = 0.1). Yet, the increase of the magnetic field causes an increase in the magnetization and consequently an increase in T C Figure 8 presents the variation of the magnetic entropy change | S M |vs. temperature for AMn 1−x Ti x O 3 (x = 0.0 and 0.1) in different applied magnetic fields. It can be seen that there is an agreement with the experimental result. Moreover, | S M |depends on the applied fields. The increase of the magnetic field causes a shift of the position of the peak to higher temperature (i.e. the peaks shift from 264 K for μ 0 H = 1 T to 266 K for μ 0 H = 5 T for the undoped sample and from 131 K for μ 0 H = 1 T to 169 K for μ 0 H = 5 T for the compound doped in titanium). Additionally, with increasing the magnetic field, the maximum magnetic entropy change S max M shows a linear increase. This reveals a much better S M to be expected when we increase the magnetic field, hence signifying that the effect of spin-lattice coupling is associated with the change in the magnetic ordering process  1 (b)). The solid lines are predicted results, and symbols represent experimental data in the samples [28]. Also, the RCP factor which corresponds to the amount of heat transferred between the cold and the hot skins in the ideal refrigeration cycle increases by increasing the magnetic field. Figure 9a, b depicts the variation of the maximum of the change entropy | S max |and the variation of RCP values vs. applied magnetic field passing from 1 to 5 T, respectively. We conclude that all samples present a clear increase in the | S max |and RCP values when the magnetic field increases and their values decrease when introducing the titanium; for x = 0.0, values of RCP are more important compared with the x = 0.1 sample. For H = 5T, samples depict not only the highest RCP values but also the important value of | S max |. We determined the specific heat C P as a function of temperature for La 0.5 Pr 0.2 Sr 0.3 Mn 1−x TiO 3 (x = 0.0 and 0.1) by using Eq. 11 in different magnetic fields; C P goes through an unexpected change of sign around T C with a positive value above T C and a negative value below the Curie temperature. The variation of the specific heat for    Table 5 The  We listed in Tables 4 and 5 the − S max M , δT FWHM , RCP, C P,H(max) ,and C P,H(min) vs. applied magnetic field. It is important to note that the other method utilized to identify the transition nature from the compounds is the | S M |. Figure 11a, b for temperature below and above the transition respectively for La 0.5 Pr 0.2 Sr 0.3 MnO 3 , it is viewed that | S M |changes to a positive value with the increase of the magnetic field, which corresponds to the magnetic transition from FM to PM states. We can see on Table 6 that we have a low S max M compared with the other manganites listed in the table, but we have a large full width at half maximum and consequently important RCP [29,30,33].
In place of M 2 vs. H /M, we can obtain the nature of transition by tracing S M / S max M as a function of θ , and we followed the model proposed by Franco et al. [34]. Their proposition is traced S M curves with different maximum applied fields which should collapse on the same universal curve in the case of a second-order phase transition [31][32][33]. In this context, the construction of this phenomenological universal curve requires the normalization of all the S M (T, μ 0 H ) curves with their respective peaks and to the rescale of the temperature axis as [35,36] θ is the rescaled temperature T r1 and T r2 are the temperatures of the two reference points that, in our study, have been chosen as those corresponding to S max M divided by 2. Figure 12 presents the magnetic entropy change of theLa 0.5 Pr 0.2 Sr 0.3 MnO 3 , measured for the maximum

Conclusion
In this research paper, we investigated the effect of substitution in the B site on the structural, magnetic and magnetocaloric properties of AMn 1−x Ti x O 3 with x = 0.0 and 0.1 synthesized using the solidstate method.
The refinement proves that all samples crystallize in the rhombohedral structure with R3c space group. In addition, samples present a second-order ferromagnetic to paramagnetic phase transition which takes place at the T C . Furthermore, based on phenomenological model. A detailed investigation of our magnetic and magnetocaloric properties samples have been studied; we can note that there is an agreement between measured magnetic entropy change and those calculated theoretically of M (T ) and − S max M at different applied fields For x = 0.0, sample presents an important − S max M and RCP comparable with