We used Monte Carlo models to look into how the surface of ferromagnetic perovskite thin films affects their magnetocaloric properties. The research discovered that film thickness and exchange coupling can change thermal magnetisation, transition temperatures, magnetic entropy change, relative cooling power, and the magnetic hysteresis cycle temperature. We look at how the lower critical temperature of perovskite ferromagnetic thin films changes with film thickness and the exchange reactions in the mass, on the surface, and between the surfaces.
The biggest change in entropy can be seen in thin-film systems at temperatures that are much lower than the point at which the magnetic phase changes. As the external magnetic field gets stronger, the maximum entropy changes. Depending on the width of the film, the relative cooling power goes up as the external magnetic field goes up. As the surface exchange coupling value goes up, the relative cooling power goes down. When the surface exchange coupling is less than the volume exchange coupling, the magnetic coercive field gets weaker as the temperature rises.
Magnetocaloric refrigeration, which uses the magnetocaloric effect, is becoming a potential technology that could replace traditional vapour compression refrigeration because it uses less energy, is smaller, and has a smaller impact on the environment. The magnetocaloric effect is mostly controlled by two important factors: the change in magnetic entropy and the change in adiabatic temperature in reaction to a change in magnetic field. Both of these are essential for getting high magnetic cooling efficiency.
Researchers have put a lot of effort into making new magnetocaloric materials in the past. The MnCoGe material has great magnetic qualities that make it easy to measure magnetocrystalline anisotropy constants up to 100 K in both perpendicular and parallel directions. The physical qualities of thin layers are very different from those of their bulk versions, as shown by both theory and experimental research.
Ising Model and Monte Carlo Simulations
The Ising model is used to describe the Hamiltonian for perovskites ferromagnetic thin films with L monolayers. The model includes interactions between nearest neighbours and an external magnetic field h. The system is made up of 1600 spins that are thought to live in unit cells. We used Monte Carlo simulations to model the Hamiltonian. We set circular free conditions on the lattice and boundary conditions in the (y, x) plane.
The energy inside each perovskites ferromagnetic thin film site is given by E = 1^N ▨H▩. The surface magnetisation (MS) is equal to (NS ∑²iλSi) and the bulk magnetisation (MB) is equal to (NB ∑²iλSi). NS = 2xN and NB = (L-2)xN. The total magnetisation of thin films made of perovskites is M = NS MS + NB MB.
These equations show how magnetic perovskites thin films are on the surface and in the bulk: χS = β(▨M2 S − ▨MS▩2) and χB = β(▨M2 B − ▨MB▩2). χ = β(▨M2▩ − ▨M▩2) is the total susceptibility of perovskites ferromagnetic thin films. Here, β = 1^kB T, T is the absolute temperature, and kB is Boltzmann’s constant.
The thermodynamic Maxwell relation (∂ S∂h) = (∂ M∂T)h can be used to figure out how a material’s magnetic entropy changes. From h not equal to zero to h equal to zero, the following changes in magnetic entropy happen:
Sm(T, h) = Sm(T, h) – Sm(T, 0) = hmax0( MT)hi dh, where hmax is the strongest magnetic field that can be applied from the outside. Hi is another name for the heat magnetisation for a constant magnetic field.
The relative cooling power (RCP) is shown as the area under the curve where ΔSm(T) changes with temperature. This is the best balance between the size of the change in magnetic entropy and the width of the peak. This is what RCP means:
RC P = ∫^Th^Tc ΔSm(T)dT, where Th is the temperature that is hot and Tc is the temperature that is cold. Tc and Th are adjacent to the half-maximum value of ΔSmax m.
Results and Discussion: Surface Effects in Perovskites
Ferromagnetic Thin Films
In this study, the heat partial and total magnetisations, as well as the magnetic susceptibilities, of perovskite ferromagnetic thin films with L = 6, R = +0.1, and h = 0.5 are given. The lower transition temperatures for surface magnetisation (MS), bulk magnetisation (MB), and total magnetisation (M) can be found at the magnetic susceptibility peaks (χS, χB, and χ), which were then figured out. The numbers that were found were tC(surface) = 4.5 and tC(bulk) = 10.55.
There is a phase diagram of the system in a plane with lines R = Js/JB and tC = TC/JB. Each curve represents a different film thickness, with L = 4, 6, 8, and 10. At the same ordinate point t B C = 12.34 and abscissa RC = 1.6, the curves meet. At these points, tC doesn’t depend on the thickness of the film. It’s more like a 3D infinite bulk system, where surfaces (001) and (00L) don’t matter.
There should be a new meaning of the RC parameter. It can be thought of as the R number at which tC doesn’t change depending on the thickness of the film. Then, tC is the lower temperature of the whole system, tB C. The ordering temperature of the film goes up as R goes up, and it’s higher than the bulk ordering temperature at B C when R is greater than RC.
Figure 7.4 shows how the magnetic entropy changes with temperature when there are different external magnetic fields h/JB = 0.5, 1.0, 1.5, and 2.0 and the film thickness L = 4 (a) and 10(b) for R = + 0.1. The largest change in magnetic entropy, Smax, goes up as the external magnetic field goes up and down as the thin layer L goes up.
The study looks into how ferromagnetic perovskites affect the surface of films of different layers and their magnetic properties. When L = 4, the absolute value of the greatest magnetic entropy change (|ΔSmax|) goes down as reduced surface coupling (R) goes up. When L = 10, on the other hand, it goes up as R goes up. This graph shows how the magnetic entropy changes with temperature for different film thicknesses (L = 4, 6, 8, 10) with R = + 0.1 (a) and + 2.1 (b) and h/JB = 1.0.
For R < 1, the decreased transition temperature goes up as the film thickness goes up, but it goes down as R > 1 increases. For both R = + 0.1 and + 2.1, the |ΔSmax| numbers go down as the film thickness goes up. For R = +0.1, the relative cooling power (RCP) number goes up as magnetic fields and film thickness go up. For R = 2.1, it goes down as film thickness goes up.
The magnetic hysteresis cycle of the bulk, the magnetic hysteresis cycle of the thin film, and the magnetic hysteresis cycle of the surface are shown for temperatures (t = 1.0, 4.2, 7.2), R = + 0.1, and R = + 2.1. When L = 8, the highest saturation magnetisation goes down as temperature goes up, and the magnetic coercive field goes down as well.
When R is less than or equal to 1.6, the magnetic coercive field goes up as the film thickness goes up and down as the film thickness goes up. The picture 7.10 shows the magnetic field of a ferromagnetic thin film compared to the exchange interactions R with L = 4 and 10.
The study looks into how the magnetic entropy change (ΔS) changes with temperature for different film thicknesses (L = 4, 6, 8, 10), with R = + 0.1 (a) and + 2.1(b) for h/JB = 1.0 and R > RC = 1.6. The hCJB value of the reduced magnetic field of the bulk system is the R value at which t C doesn’t change with film thickness.
It is also looked at how RP changes with an outside magnetic field for different film thicknesses (L = 4, 6, 8, 10 and R = +0.1 and L = 8). The total magnetic hysteresis cycle of the ferromagnetic thin film, the magnetic hysteresis cycle of mass B, and the magnetic hysteresis cycle of surface C are all shown for temperatures (t= 1.0, 4.2, 7.2, R = +0.1, and L = 8).
The magnetic coercive field was seen to decrease as the film thickness increased at a constant temperature and as surface coupling decreased. This is similar to what other studies have found, like when they looked at the superparamagnetic behaviour in very thin CoNi layers within electrodeposited CoNi/Cu multilayer nanowires. This points to a similar pattern in magnetic properties that is linked to changes in film thickness and temperature in different magnetic systems.
In the end, the study gives us useful information about the magnetic features of perovskites and how they affect the surface. The results show that the magnetic coercive field weakens as the film thickness increases and surface coupling drops. This is a general trend in magnetic properties that is linked to film thickness and temperature changes in different magnetic systems.
Conclusions
Monte Carlo models are used to look into how the lowered transition temperature, magnetic entropy change, and relative cooling power behave in thin ferromagnetic films. It finds a critical number (RC) for the R parameter above which tC doesn’t depend on the thickness of the film. The research also shows that |ΔSmax| goes up when the external magnetic field is stronger and down when the film thickness is thinner. The study also shows how the different things that affect the magnetic properties of these thin films work together. As the temperature and film layer go up, the magnetic coercive field goes down. On the other hand, it goes up when the temperature stays the same and surface coupling goes down.
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