Comparative examination of the physical parameters of the sol gel produced compounds La0.5Ag0.1Ca0.4MnO3 and La0.6Ca0.3Ag0.1MnO3

In this paper, the physical characteristics of La0.5Ag0.1Ca0.4MnO3 and La0.6Ca0.3Ag0.1MnO3 compounds have been studied. Structural analysis by XRD showed that both samples crystallize in an orthorhombic structure. For the La0.5Ag0.1Ca0.4MnO3 sample it can be seen that there are two bands: the first is due to the stretching Mn–O bond the υs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsilon }_{s}$$\end{document} vibration mode, relates to the internal motion of a length-changing Mn–O, whereas the second corresponds to the υb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsilon }_{b}$$\end{document} bonding mode, which is sensitive to a change in the Mn–O–Mn angle. For the compound La0.6Ca0.3Ag0.1MnO3 the υb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsilon }_{b}$$\end{document} band is absent. The magnetic measurements show that the two compounds have a single transition from the PM state to the FM state with an increase in the Curie transition temperature Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document} for the compound La0.6Ca0.3Ag0.1MnO3. Similarly, the substitution of silver in calcium increases the value of the magnetization at low temperature. We also studied the magnetocaloric effect of our compounds. This study shows a significant change in magnetic entropy ΔSM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {S}_{M}$$\end{document} that took place around their magnetic transition temperatures Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document}. Under the influence of a 5 T magnetic field. The largest fluctuation in magnetic entropy is in the order of − 8.67 J/kg·K for the compound La0.6Ca0.3Ag0.1MnO3 this value is considered significant. The magnetocaloric results indicate that the compound La0.6Ca0.3Ag0.1MnO3 is the best sample which has a large RCP which suggests its good candidate in the field of magnetic cold. Based on the Banarjee criterion and Landau theory, a second-order transition is observed for both samples in the vicinity of the Curie transition Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document}. The experimentally obtained value of ΔSM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta S}_{M}$$\end{document} is smaller than the theoretically calculated one, which proves that the transition is an unconventional transition even under the influence of a 5 T magnetic field.


Introduction
Manganites of structure Ln 1-x A x MnO 3 (with Ln: rare earths and A: divalent element) have interesting physical properties and enormous technological interest in various fields of application. These intrinsic features are often described in these highly correlated electron systems by the indirect exchange interactions between the Mn +3 and Mn +4 ions, the average ionic radius of site A, and the magnetic and orbital disorder (Dkhilalli et al. 2018a, b, c;Enneffati et al. 2018). In this structure manganese has a mixed valence Mn +3 ∕Mn +4 . Indeed, the trivalent element is substituted Ln 3+ by a divalent or monovalent element leads to oxidation of the Mn 3+ ions ([Ar] 3d 4 ) into Mn 4+ ions ([Ar] 3d 3 ). The La 1-x Ca x MnO 3 system is one of the most studied compounds in recent years due to its rich magnetic and electrical behavior (Enneffati et al. 2019). Previous studies carried out in our laboratory (Gharbi et al. 2021; on manganites of the perovskite type of general formula La 0.5 Ca 0.5 MnO 3 substituted by silver in the A site revealed that 10% silver is sufficient to destroy the state charge order and increase ferromagnetic interactions with an increase inT c . This rise is due to the shift in the Mn-O-Mn angles caused by the overlap of the manganese ions' 3d orbitals and the oxygen ions' 2p orbitals, which is primarily responsible for the magnetic interaction in this system (Walha et al. 2004(Walha et al. , 2009Hamdi et al. 2017a, b;Assoudi et al. 2018a;Felhi et al. 2018). To complete and continue our work we have to study the physical properties of the compounds La 0.5 Ag 0,1 Ca 0.4 MnO 3 and La 0.6 Ca 0.3 Ag 0.1 MnO 3 using the sol-gel method given the important magnetocaloric properties of the compounds synthesized in this manner (Rietveld 1967;Rodriguez-Carvajal and FULLPROF, xxxx;Goldshmidt 1927;Shannon 1976).

Results and discussion
XRD patterns for both samples were realized at room temperature and analyzed with the Rietveld refinement technique. La 0.5 Ag 0.1 Ca 0.4 MnO 3 and La 0.6 Ca 0.3 Ag 0.1 MnO 3 samples crystallize in the orthorhombic structure with Pbnm space group. Typical examples of the observed and calculated diffraction profiles for both samples are given in Fig. 1.
In order to determine the modes of vibrations and to identify the different types of bonds present in the structure of the samples, a study by infrared absorption spectroscopy using an FTIR Spectrum spectrometer (Fig. 2) was carried out. We observe two bands in the La 0.5 Ag 0.1 Ca 0.4 MnO 3 sample: the first at 594 cm −1 corresponds to the Mn-O bond stretching the vibration mode s , including the internal movement d caused by a change in Mn-O bond length, and the second at 420 cm −1 corresponds to the b vibration mode, which is sensitive to a change in the Mn-O-Mn angle (Shelke and Deshpande 2017;Arulraj and Rao 1999;Shivakumara and Bellakki 2009). A single band at 590 cm −1 is seen in the La 0.6 Ca 0.3 Ag 0.1 MnO 3 sample, which may be ascribed to the Mn-O bond stretching the s vibration mode s .
The Mn ion is surrounded by six oxygen ions in the perovskite structure. A vertical axis was considered, connecting the Mn ion to the two oxygens. The s vibration consists of the movement of Mn ion and oxygen by changing the length of the Mn-O 1 band while the b binding vibration occurs when there is a change in the O 1 -Mn-O 2 angle.
To investigate the magnetic characteristics of compounds, we did magnetization measurements as a function of temperature and applied magnetic field of 0.05 T, as well as magnetization measurements as a function of applied magnetic field at various temperatures, M(H) . The undoped compound La 0.6 Ca 0.4 MnO 3 has been studied in our laboratory (Gharbi et al. 2021). It is indexed in the P nma orthorhombic structure. It has a curie temperature of 269K.
The thermal evolution of the magnetization M(T) of the two samples which is represented in Fig. 3a shows that all the compounds present a continuous magnetic transition thus confirming on the one hand the good crystallization of the samples and on the other hand the homogeneous distribution of substituted ions. Additionally, the two silver-substituted compounds display a wide transition from the paramagnetic to the ferromagnetic state (FM) when the temperature lowers, and the magnetization value of the compound La 0.5 Ag 0.1 Ca 0.4 MnO 3 is less than that of the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 (Ying et al. 2011;Itoh et al. 1995).
By examining the curve Fig. 3b dM∕dT in relation to temperature, we also note that silver's replacement for lanthanum causes a reduction in the T c compared to that of calcium by silver. The difference between these two values can be explained by the valence effect seen by the weakening of the double exchange's ferromagnetic contacts in the molecule La 0.5 Ag 0.1 Ca 0.4 MnO 3 (Baaziz et al. 2015). Indeed, the magnetic behavior of manganites is directly linked to the Mn +3 /Mn +4 ratio.
So, to favor the existence of a ferromagnetic phase at sufficiently high temperatures, the double exchange interaction must be favored, which therefore requires a minimum fraction of Mn +4 . This ferromagnetism is optimum for 2 3 Mn +3 and 1/3 Mn +4 compositions according to the phase diagram of La 1-x Ca x MnO 3 , which explains this slight increase in T c for the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 since it has a valence Mn +3 ∕Mn +4 = 1 according to the neutrality equation Mn +3 0.5 Mn +4 0.5 and consequently 50% of Mn +4 while the compound La 0.5 Ag 0.1 Ca 0.4 MnO 3 has a Mn +4 level of 60% according to the neutrality equation Mn +3 0.4 Mn +4 0.6 . Magnetization isotherms as a function of applied field are seen in Fig. 4. As can be observed, magnetization rises as a function of the applied magnetic field and it reaches saturation at the end of a field of the order of 0.5 T, To ascertain the magnetic transition's nature, conventional Arrott plots of M 2 vs 0 H/M demonstrate a positive slope indicative of a second-order FM-PM transition (Fig. 5). In the vicinity of the Curie temperature, the linear curves which pass through the origin coincide with temperatures close to those deduced from the dM∕dT curve. These temperatures are determined at 270K and 261K respectively for La 0.6 Ca 0.3 Ag 0.1 MnO 3 and La 0.5 Ag 0.1 Ca 0.4 MnO 3 .
The magnetic entropy ΔSM , which is proportional to the magnetic degrees of freedom, fluctuates according to the applied magnetic field and the sample's magnetic order. The where T is the temperature, H 1 and H 2 denote the magnetic applied fields, with H 1 ≤ H 2 because the magnetic fields H change from 1 to 5 T ( H 1 = 1 , H (Ezaami et al. 2017) where 0 the magnetic constant (permeability of free space or vacuum permeability), M the magnetization measurement and M(T) the magnetization versus temperature, the magnetization values M i and M i+1 measured in a magnetic applied field H j at temperatures T i and T i+1 , respectively, and ΔS M (the isothermal magnetic entropy change). For each temperature, the air is computed by dividing the temperature difference between the two isotherms around the temperature in question by the required field range.
The development of −ΔS M (the experimental magnetic entropy change) as a function of temperature is shown in for several application industries (Fig. 6). It is noticed that when the applied magnetic field is increased, the absolute value of the maximum Magnetic transitions may be observed using curves plotting the change of magnetic entropy with temperature. An extremum of magnetic entropy variation can be observed around a magnetic transition following a change in the magnetic order within the material. The −ΔS Max (T) curves show an increasing trend for temperatures below the Curie temperature, then reach maximum values for T = T c . On the other hand, the maximum of the magnetic entropy increases with the applied magnetic field. We note −ΔS Max that presents a maximum in the vicinity of T c for the two compounds and that −ΔS Max is greater at the level of compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 . Under the influence of a 2 T magnetic field in the vicinity of T c , ΔS Max M reaches values of the order of 2.02 J/kg K for the compound La 0.5 Ag 0.1 Ca 0.4 MnO 3 whereas that in the case of compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 is of the order of 5.55 J/kg K. This magnetic entropy maximum −ΔS Max is a critical requirement for categorizing a material as a suitable candidate for magnetic refrigeration, giving it the benefit of being a good candidate for magnetic refrigeration near ambient temperature.
The entropy variation between the two compounds can be interpreted by the nature of the ferromagnetic-paramagnetic transition which is much slower than that observed in the case of the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 .
The relative cooling power, or RCP (Relative Cooling Power), which is defined as the product of the ΔS max M and the width at mid-height T FWHM of the curve ΔS M (T, H) , has been shown to be a helpful measure for assessing a material's suitability for magnetic refrigeration. The following relationship defines this metric, which represents the amount of heat that may be transported between a refrigerator's hot and cold sources (Assoudi et al. 2018b;Wang and Appl 2000;Rostamnejadi et al. 2011). where T FWHM the full width at half maximum.  Table 1.
We note that the RCP values of the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 are greater than those of the compound La 0.5 Ag 0.1 Ca 0.4 MnO 3 which suggests its good candidacy in the field of magnetic cold All the samples show an interesting factor of the RCP around the Curie transition temperature T c . Other substances have also been reported to have this magnetocaloric action (Felhi et al. 2018;Walha et al. 2009).
The change in specific heat or heat capacity ΔC P (heat capacity changes) was then computed for the two compounds from the entropy using the following formula.
The fluctuation in specific heat as a function of temperature is shown in Fig. 8 for various levels of the applied magnetic field, ranging from 1 to 5 T. It is plain to observe that as the temperature is reduced, the value of ΔC P quickly shifts from positive to negative (Gschneidner et al. 2005a). ΔC min∕max P values grow as μ 0 H increases .   Walha et al. (2009) By altering the magnetic field μ 0 H as a function of the magnetization, the temperature dependence of the landau coefficients A(T) , B(T) , and C(T) is derived (Gschneidner et al. 2005b;Regmi et al. 2009).
where A , B and C are temperature-dependent expansion coefficients or the Landau coefficients. The results of this adjustment are shown in Fig. 9 for the two compounds La 0.5 Ag 0.1 Ca 0.4 MnO 3 and La 0.6 Ca 0.3 Ag 0.1 MnO 3 . As predicted, A is positive near T c (curie temperature) and the value of B is positive at T c , confirming the transition's second order nature.
By differentiating the magnetic component of the free energy with respect to temperature, one may derive the appropriate magnetic entropy (Pankratov et  with M 0 being the value of the magnetization measured in the absence of a magnetic field. The findings indicate that our materials display a magnetic transition of second order. Figure 10 illustrates the theoretical findings and actual data for various applied magnetic fields. The research indicates unequivocally that magnetoelastic coupling and electron interaction both contribute significantly to magnetic entropy and its temperature dependence for both samples. Additionally, the experimentally determined value of S M is less than the theoretically estimated value, indicating that the transition is an unusual one even when a 5 T magnetic field is supplied. Chandra et al. (2012) recently investigated the magnetic and magnetocaloric characteristics of LaMnO 3-δ and discovered that the observed ΔS M is less than the predicted one. This model does not account for the Jahn-Teller distortion, and the exchange interactions accurately predict the observed change in magnetic entropy as a

Fig. 10
The theoretical findings and actual data for various applied magnetic fields function of temperature. It is thus necessary to include these interactions into the magnetocaloric effect estimated using the indirect technique in order to modify this model.

Conclusion
In this paper, we studied the physical properties of La 0.5 Ag 0.1 Ca 0.4 MnO 3 and La 0.6 Ca 0.3 Ag 0.1 MnO 3 compounds. Structural analysis by XRD showed that both samples crystallize in an orthorhombic structure. The magnetic measurements show that the two compounds have a single transition from the PM state to the FM state with an increase in the Curie transition temperature T c for the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 . Similarly, the substitution of silver in calcium increases the value of the magnetization at low temperature.
We also studied the magnetocaloric effect of our compounds. This study shows a significant change in magnetic entropy ΔS M that took place around their magnetic transition temperatures T c . The magnetocaloric results indicate that the compound La 0.6 Ca 0.3 Ag 0.1 MnO 3 is the best sample which has a large RCP which suggests its good candidate in the field of magnetic cold. based on the Banarjee criterin and Landau theory, a second-order transition is observed for both samples in the vicinity of the Curie transition T c . The experimentally obtained value of ΔS M is smaller than the theoretically calculated one, which proves that the transition is an unconventional transition even under the influence of a 5 T magnetic field.
Funding The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Conflict of interest
The authors declare that they have no conflict of interest.