Monte Carlo models are used to look into the structure of layered manganite La2SrMn2O7 in the work. It is found that temperatures change the system’s heat magnetisation, and a magnetic change from ferromagnetic to paramagnetic is seen. At the transition point, the second-order phase change can also be seen. It was found that the magnetic entropy changes of La2SrMn2O7 bilayer manganite depend on the temperature when different magnetic fields are applied. Also given is how the relative cooling power of La2SrMn2O7 bilayer manganite changes with the magnetic field. It is also given the magnetic hysteresis cycle of the two-layer manganite group. Around the transition point, superparamagnetic behaviour can be seen.
LaSr2Mn2O7 has been studied a lot because it has huge magnetoresistance, charge ordering, and different magnetic phases. These materials could be used in porous cathodes of solid oxide fuel cells, which could make the process of turning energy into electricity more efficient. Researchers have looked into the electronic structure and magnetic arrangements of LaSr2Mn2O7, a double-layered manganite that has 50% holes added to it. The study also looks into how the electrical properties of LaSr2Mn2O7 change depending on the particle size. One more thing that is looked at is the magnetic properties of LaSr2Mn2O7 with 200 nm grains. The chapter book is divided into several parts, such as an introduction to the model and theory, the method that was used, the results and a review of the magnetic qualities, and finally, the findings.
Ising Model and Monte Carlo Simulations
It crystallises in tetragonal lattices with a = 3.868 and c = 20.205 Å, and the space group is I4/mmm. Positional values of La, Sr, Mn, and O in LSMO are used to show the structure of the system as two layers. The Hamiltonian that describes our molecules using the Ising model includes interactions between close neighbours and an outside magnetic field h. We used the Full-Potential Linear Augmented Plane Wave to find the first, second, third, and fourth closest neighbours.
It is thought that the La2SrMn2O7 bilayer manganite system, where L = 20, lives in unit cells and has a total of 6260 spins, with 20 bilayers. To model the Hamiltonian, Monte Carlo simulations were used. In the plane (a, b), circular boundary conditions were put in place, and the c-axis was left open. To do the Monte Carlo update, random spins were picked and then turned using the Metropolis method and Boltzmann-based chance.
In this program, the internal energy per site E is of LSMO bilayer manganite is found, along with its magnetisation, changes in magnetic entropy, and the measure of its relative cooling power (RCP). If you know ΔSm(T, h) = ∑i (∂ M∂T) hi, then you know that the bilayer manganite is magnetocaloric and magnetic.
Magnetic and Magnetocaloric Properties of Bilayer
Manganite System
The study uses Monte Carlo to look into the magnetic and magnetocaloric features of the La2SrMn2O7 bilayer manganite system. When the temperature goes up, the magnetic magnetisation of LSMO bilayer manganite goes down, but it goes up when the external magnetic field goes up. It has been found that the transition temperature, which is the lowest point in dM/dT, is 213.76 K. At this crossover point, the second-order phase change takes place.
The change in magnetic entropy is affected by both the temperature and the external magnetic field. As the temperature gets closer to the transition temperature, (−ΔS) goes up and reaches its highest point. The highest magnetic change entropy is 0.39 J/kg · K for h = 1, 3, and 5 T, and it’s 1.23 J/kg · K for h = 3 T and up. To get a number like this, use Ref. [19], which is for a weak magnetic field.
This method has also been found to have a big magnetocaloric effect. For instance, it was found that La1.4Sr1.6Mn2O7 had a significant magnetic entropy change of 16.8 J/kg K when the magnetic field changed by 5.0 T. This change was much bigger than the change found for pure Gd when the magnetic field changed by the same amount.
When the temperature stays the same, the field dependence of the relative cooling power of LSMO bilayer manganite goes up as the external magnetic field gets stronger. RCP can go as high as 11 J/kg when h = 5T.
In Figure 6.6, you can see the magnetic hysteresis cycle of LSMO bilayer manganite at temperatures T = 160, 190, 213, and 220 K. As the temperature rises, the magnetic coercive field and remanent magnetisation drop until they are equal to zero near the transition point. When T = 213 and 220 K, superparamagnetic behaviour is seen.
Conclusions
The magnetic and magnetocaloric features of La2SrMn2O7 are looked at in this chapter using a Monte Carlo calculation. By looking at homogeneous magnetic behaviour, the phase shift is proven to be of a second order. As the external magnetic field gets stronger, the greatest changes in magnetic entropy get bigger, and so does the relative cooling. As the temperature goes up, the magnetic coercive field and remanent magnetisation go down. Around the transition point, superparamagnetic behaviour is seen, which shows that the phase change is a second order event.
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