The Inverse and Conventional Magnetocaloric Effects in Ni0.4Cu0.2Zn0.4Fe2-xDyxO4 Nanoferrites Over an Extraordinary Temperature Range

The magnetocaloric effect (MCE) of Ni0.4Cu0.2Zn0.4Fe2-xDyxO4 (x = 0.02, 0.03, and 0.04) nanoferrites is simulated using a phenomenological model. The analysis indicates that the MCE of Ni0.4Cu0.2Zn0.4Fe2-xDyxO4 nanoferrites is strongly influenced by Dy content in both conventional and inverse MCE. For conventional MCE, the full-width at half-maximum (δTFWHM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta {\text{T}}_{{{\text{FWHM}}}}$$\end{document}) has significant values, ranging between 200 K and 258 K for Ni0.4Cu0.2Zn0.4Fe2-xDyxO4 nanoferrites. However, for inverse MCE, δTFWHM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta {\text{T}}_{{{\text{FWHM}}}}$$\end{document} ranges between 25 and 55 K. The MCE of the Ni0.4Cu0.2Zn0.4Fe2-xDyxO4 system covers an extensive temperature range and is a particularly interesting prospect for nitrogen and hydrogen liquefaction.


Introduction
The magnetocaloric effect (MCE) is a magneto-thermodynamic phenomenon that arises in the absorption or generation of heat by such magnetically ordered material when the applied magnetic field (H exe ) is changed. [1][2][3][4][5] Because of the advantages of magnetic refrigeration (MR) including environmental safety, higher efficiency, and the ability to be implemented in a wide range of temperatures, it has become an appealing replacement for traditional refrigeration systems. [6][7][8][9][10][11] Many decades have been spent studying a broad range of materials that demonstrate acceptable magnetocaloric (MC) characteristics at ambient or even low temperatures. 9,12-18 MR could be used for gas liquefaction, specifically helium, nitrogen, and hydrogen liquefaction, as well as for research activities and low-temperature space applications. 19 MR reflects the concept of applying MCE to MC material at temperatures near that of a magnetic phase transition. [14][15][16][17][18][19] An initial response of adiabatic demagnetization occurs in traditional MCE as a cooling action in MC material, which is carried out with the abrupt removal of the H exe . [20][21][22][23][24] However, adiabatic magnetization can cool MC materials that experience a sudden increase in the H exe , which is called an inverse MCE. 4 This inverse MCE is seen in antiferromagnetic (AFM) materials over the AFM transition temperature range.
Magnetic nanoparticles (MNPs) are an excellent replacement for bulk MCE materials due to the ease of assembly in the form of thin film and other desirable features, including their influence over the ∆S M throughout the superparamagnetic-blocking transition. 24 Theoretically, decreasing the particle size to nearer the single magnetic domain enhances ∆S M by many orders of magnitude when contrasted with ∆S M in bulk materials. 24 Furthermore, the high surface area of nano-materials would enhance the exchange of heat with the surroundings, and it would be possible to modify the exchange of heat between MNPs and the surroundings by carefully designing core structures. Furthermore, different MNP sizes have the potential to achieve a broader range of cooling. 25,26 The Ni-Cu-Zn ferrite is a soft ferrite with high T MPT , large electrical resistivity and extreme permeability in the radiofrequency range. Ni-Cu-Zn ferrites are used primarily as transformer cores, inductors, recording heads, and deflection yokes. 27,28 Optimizing NiCuZn ferrites by modifying the portions of metal ions in the formula or doping with new metals has recently been investigated. When the ferric ion was partially replaced with RE ions (Gd 3+ Eu 3+ , Sm 3+ , and Pr 3+ ), a distortion in the crystal structure of the Ni 0.4 Cu 0.2 Zn 0.4 ferrite was noted, as was an improvement in its magnetic properties. 29 Almessiere et al. used the sol-gel method to prepare Ni 0.4 Cu 0.2 Zn 0.4 Fe 2-x Dy x O 4 (x ≤ 0.04) nanoferrites, which showed superparamagnetic behaviour and broadly second-order FM-paramagnetic phase transitions for all samples, along with an AFM-paramagnetic phase transition at extremely low temperatures. 30

Theoretical Considerations
The PM provides the relationship between magnetization (M) and temperature (T) as follows 31,32 : where M i is an initial value of magnetization at the FM-paramagnetic or AFM-paramagnetic transition, and M f is a final value of this transition as shown in Fig. 1 for FM or AFM phase, and  Fig. 1 The dependence of isofield magnetization vs temperature.  nanoferrites could be operated in MR that uses magnetization and demagnetization processes to exploit both positive and negative magnetic entropy variations. |∆S Max | is significantly reduced when the Dy content is high. The fact that Dy +3 ions are favoured to exist in the B sites, which can be attributed to their large ionic radii, could explain this decreasing trend. As a result of the Fe 3+ replacement by Dy 3+ , the crystal symmetry is reduced, implying that

Results and Discussion
the distance between Dy-O will be smaller than the distance between Fe-O. 33 Consequently, some of the corresponding ions display aligned antiparallel moments with regard to others in these sites, causing a drop in net magnetic moments just on B sites. As Dy 3+ content increases, further cations on B sites exhibit antiparallel moments. To put it another way, the decrease in |∆S M | at high content in samples is due to surface spin effects and cation distribution on various sites. Despite the fact that magnetic moments are no longer directed linearly, nonlinear spins of magnetic ions exist due to spin frustration. 33 The increase in migration of Fe 3+ cations from tetrahedral to octahedral sites with the goal of occupying the increasing Dy 3+ ions causes the reduction drop in the |∆S M |. The increased presence of Fe 3+ cations in octahedral B sites due to site preference causes an increase in spin canting and antiparallel spin coupling, reducing the |∆S M | and weak super-exchange interactions between tetrahedral and octahedral sites, lowering the magnetization. 34 Furthermore, the ionic radii for various elements, and also the critical A-B super-exchange interactions between many magnetic ions, could be used to deduce the influence of Dy 3+ ions on magnetic characteristics. Dy 3+ ions have an ionic radius of 0.912 Å, indicating that they prefer to be found on B sites. The ionic radii that are subjected to substitution differ greatly, causing disorder in the electronic states and internal strains in the crystal structure. This has an impact on the A-B super-exchange interactions between metal sites A and B. 35,36 Furthermore, variations in the drop in |∆S M | at high Dy 3+ content can be explained by crystallite size variation. Indeed, as the Dy 3+ content increases, the crystallite size decreases, resulting in a reduction in magnetization and, as a result, a decrease in |∆S M |. The |∆S Max | and full-width at half-maximum ( T FWHM ) of the S M curve are used to account for RCP as follows.
where T FWHM can be obtained as follows: For conventional MCE, the calculations show that T FWHM has significant values, ranging between 200 K and 258 K for Ni 0.4 Cu 0.2 Zn 0.4 Fe 2-x Dy x O 4 nanoferrites under ΔH of 0.01 T. However, for inverse MCE, the range of T FWHM is between 25 K and 55 K. Furthermore, for conventional MCE, RCP is between 0.05 J/Kg and 0.08 J/Kg, Furthermore, they have high resistivity, small hysteresis, low loss of eddy current, and the energy loss is negligible. 30 The MCE and the electrocaloric effect both contribute to the future of refrigeration technology. 37 4 nanoferrites are an interesting possibility for MR because they cover a wide temperature range, especially liquefaction of nitrogen and hydrogen, even at room temperature.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

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