Investigations on Strong-Tuned Magnetocaloric Effect in La0.5Ca0.1Ag0.4MnO3

The magnetocaloric effect (MCE) of La0.5Ca0.1Ag0.4MnO3 (LCAMO) is simulated using a phenomenological model (PM). The LCAMO MCE parameters are calculated as the results of simulations for magnetization vs. temperature at different values of external magnetic field (H ext). The temperature range of MCE in LCAMO grew as the variation in H ext increased, eventually covering the room temperature at high H ext values. The MCE of LCAMO is tunable with the variation of H ext, proving that LCAMO is practically more helpful as a magnetocaloric (MC) material for the development of magnetic refrigerators in an extensive temperature range, including room temperature and lower and higher ones. The MCE parameters of LCAMO are practically greater than those of some MC samples in earlier works.


INTRODUCTION
The need to solve the problem of emission of hazard gases, which come out of conventional vapor refrigerators, results in increased interest in functioning magnetic refrigerator (MR), the idea of which depends on functioning magnetocaloric effect (MCE) (Dhahri et al., 2014;El-Sayed and Hamad, 2019a;El-Sayed and Hamad, 2019b;Ahmed et al., 2021a, Ahmed et al., 2021bHamad et al., 2021;Jebari et al., 2021), because the MR provides high efficiency for cooling without any negative impact on the environment and has low energy consumption, availability of mechanical stability, and fewer noise events during cooling operation (Dhahri et al., 2015;Hamad, 2015a;ErchidiElyacoubi et al., 2018a, ErchidiElyacoubi et al., 2018bHamad et al., 2020;Sharma et al., 2020;Belhamra et al., 2021). MCE is described as a change in magnetic entropy (ΔS M ) with a variation in the external magnetic field (H ext ) exerted on the material, causing a change in temperature (Masrour et al., 2016;ErchidiElyacoubi et al., 2018c;Kadim et al., 2020, Kadim et al., 2021a, Kadim et al., 2021b. Numerous research over decades have studied various magnetic materials to discover their suitability as magnetocaloric (MC) materials suitable for the MR industry (Hamad, 2015b;Masrour et al., 2017;Jebari et al., 2021;Labidi et al., 2021). It is preferable to use MC materials that have a magnetic transition type of the second degree with a suitable Curie temperature (θ C ) as appropriate for use in a wide temperature range, including room temperature (Choura-Maatar et al., 2020;Henchiri et al., 2020;Laajimi et al., 2020). The current efforts are directed towards the use of manganite as an effective substance in MRs due to its great chemical stability during frequent use, lack of eddy current, ease of preparation, high electrical resistance, and the possibility of improving their properties through doping and changing the oxygen content (Alzahrani et al., 2020;Choura-Maatar et al., 2020;Henchiri et al., 2020;Laajimi et al., 2020). Felhi et al. prepared La 0.5 Ca 0.1 Ag 0.4 MnO 3 (LCAMO) via the ceramic method and reported an increase in H ext and an increase in broad ferromagnetic (FM) phase transition of LCAMO covering room temperature under high H ext (Jeddi et al., 2020).
These results motivate us to investigate the MCE of LCAMO, expecting that the MCE of LCAMO covers a large range of temperatures, especially cryogenic temperature and room temperature. Furthermore, it is believed that LCAMO, as a manganite, has low material processing costs, high chemical stability, and high resistivity, which are advantageous for reducing the overall eddy current heating. In this research, the MCE of LCAMO is studied using a phenomenological model (PM) to simulate the isofield magnetization vs. temperature curves, concluding with simulated ΔS M , heat capacity change (Δ C P,H ), and relative cooling power (RCP).

THEORETICAL CONSIDERATIONS
According to PM, as described in Hamad (2012Hamad ( , 2015cHamad ( , 2015d, the magnetization (M) vs. temperature is simulated by: where M i and M f are values of magnetization at the onset and finalization of the FM paramagnetic transition as pointed out in Figure 1, respectively.
The numerical evaluation of ΔS M of LCAMO under H ext variation (ΔH) can be derived from Maxwell's relation and derived from Eq. 1 as follows:  The full-width at half-maximum (δT FWHM ) of LCAMO can be given as follows: A magnetic cooling efficiency of LCAMO is expected by considering the magnitude of |ΔS Max (T, H max )| and δT FWHM (Hamad, 2012). RCP is calculated as follows: The Δ C P,H of LCAMO can be given as follows (Hamad, 2012):

RESULTS AND DISCUSSION
At values of H ext <5 T, there are two magnetic transitions of LCAMO, as can be observed in Figure 2, at two different temperatufvariation, which is about 57% of the correspondingres. It is possible that this is due to the presence of a canted FM phase in the FM matrix, which can be attributed to the additional Ag content (Jeddi et al., 2020), thus expecting two peaks in the ΔS M curves. However, at H ext = 5 T, it seems like a single magnetic transition of LCAMO, expecting a single peak in the ΔS M curve. It is possible that this is due to the presence of a strong interatomic double exchange interaction at H ext = 5 T. To simulate the MCE of LCAMO, the PM parameters (M i , M f , ɵ c , β, and α) of LCAMO for each magnetic transition were determined directly from experimental data (isofield magnetization vs. temperature) as in Jeddi et al. (2020). We can see from Figure 2 that there is a good agreement between the experimental and theoretical results of M(T), confirming the good fit of this model for simulating the MCE of LCAMO. This work demonstrates the good coincidence between the experimental data and the continuous curves given by PM, indicating that this model allows us to predict the MCE for LCAMO under different magnetic fields. The M(T) curves of LCAMO demonstrate the magnetic transition from the FM phase to a paramagnetic one under different magnetic fields. The θ C increases as H ext increases due to the increased alignment of the local spins, resulting in an increase in the interatomic double exchange interaction. As shown in Figure 3A, there are two peaks in the ΔS M (T) curves when H ext <5 T. However, at H ext = 5 T, there is a single peak in the ΔS M curve due to the large interatomic double exchange. ΔS M reaches a peak of 2.75 J/kg K. Though the maximum ΔS M is 2.75 J/kg K upon 5T applied field variation, which is about 57% of the corresponding value of the compound that belongs to the same system as La 0.5 Ca 0.2 Ag 0.3 MnO 3 (ΔS Max = 4.8 J/kg K upon 5 T), the value of RCP (273.5 J/kg upon 5 T) is larger, and the ΔS M distribution of LCAMO is much more broad than that of La 0.5 Ca 0.2 Ag 0.3 MnO 3 (RCP = 168 J/kg δT FWHM = 35 upon 5 T), covering a wider range of temperature (Felhi et al., 2019). Figure 3B shows that ΔS M (T) was calculated by Maxwell relation from experimental isothermal magnetization as a function of H in Ref. 31, and ΔS M (T) was calculated by PM, ranging between 240 and 270 K and covering the highest temperature transition. There is a good agreement and approach between the calculated results of both Maxwell relation and PM. Therefore, these results confirm that Eq. 4 still holds at ΔH of 0.5, 1, 3, and 5 T.   Frontiers in Materials | www.frontiersin.org February 2022 | Volume 9 | Article 832703 Figure 4 shows that ΔC P,H (T) has an inverse change from a negative change to a positive one at around θ C for each magnetic transition, causing a modification in the total specific heat. This oscillating temperature dependence of ΔC P,H (T) at different temperatures is a reflection of ΔS M (T) behavior. The behavior of | ΔS M | and ΔC P,H (T) curves suggests how the range of temperature for functioning LCAMO in the MR can be expanded. It is clear that the | ΔS M | and ΔC P,H peaks of LCAMO extend over a large temperature range. This temperature range of |ΔS M | and ΔC P,H expanded with increasing variation in H ext , i.e., the peaks broaden, covering room temperature upon high values of ΔH. This indicates that larger |ΔS M | and ΔCP, H are expected at higher values of ΔH. Moreover, the variation of H ext allows the tuning of θ C of LCAMO. This tunable θ C makes LCAMO practically more helpful for the development of MRs. Figures 5-8 show the values of |ΔS Max |, δT FWHM , RCP, and ΔC P,H(Max) (maximum value of ΔC P,H ) for LCAMO, respectively. It is clear that |ΔS Max |, RCP, and ΔC P,H(max) show a general increase with an increase in ΔH due to enhancing the variations of alignment in the local spins with an increase in ΔH, resulting in an increase in MC properties.
These large values of |ΔS Max |, δT FWHM , RCP, and ΔC P,H(Max) in LCAMO prevailed as well in perovskite manganite due to the strong coupling between spin and lattice (Dhahri et al., 2008). Since lattice change is associated to magnetic transition in the manganite, this caused a further change in the magnetism of manganite (Dhahri et al., 2008). Furthermore, the bond distance of <Mn-O> plus bond angle <Mn-O-Mn> changes to favor the spin ordering with a high value of H ext , leading to enhanced |ΔS Max |, δT FWHM , RCP, and ΔC P,H(Max) in LCAMO (Radaelli et al., 1995;Hamad, 2015b). Table 1 gives a comparative importance of the MCE parameters of LCAMO with those of various materials in terms of the high values of ΔH in previous works (Álvarez-Alonso et al., 2013;Hamad, 2013;Saadaoui et al., 2013;Ho et al., 2014;Bhumireddi et al., 2015;Boutahar et al., 2015;Jerbi et al., 2015;Gupta and Poddar, 2016;Mansouri et al., 2016;Oubla et al., 2016;Long et al., 2018;Biswal et al., 2019;El Boubekri et al., 2020). The MCE parameters of LCAMO are significantly larger than some MCE parameters of MC samples in the corresponding values of ΔH and the higher ones. From this comparative image, we conclude that LCAMO can function as a favorable MC magnet for the MR.

CONCLUSION
Based on thermodynamic calculation via PM, the MCE of LCAMO is simulated under different values of variation in H ext . The MCE of LCAMO is strongly tunable with the value of the variation of H ext . Therefore, LCAMO can be used over a wide temperature range as an effective material for MR, covering a large range of temperatures, including room temperature and lower and higher ones. The MCE of LCAMO is tunable with the variation of H ext , proving that LCAMO is practically more helpful as a MC magnet for the development of MRs in an extensive temperature range, including room temperature. The values of the MCE parameters of LCAMO are practically greater than the MCE ones of some MC samples in earlier works.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

AUTHOR CONTRIBUTIONS
All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.