The work on Pr0.65Sr0.35MnO3 perovskite used first principle calculations and Monte Carlo simulations to look into its electronic and magnetic properties, as well as its magnetocaloric effect. The research discovered that Pr0.65Sr0.35MnO3 perovskite is ferromagnetic and halfmetallic, with 100% spin polarisation. This is important because it explains the compound’s huge magnetoresistance. The first main calculations gave us the magnetic moment and the thermal variation of magnetisation. These numbers told us a lot about the magnetic behaviour of the material and how it changes with temperature.
We used Monte Carlo simulations to look at how the magnetic entropy change and the adiabatic temperature depend on temperature. This let us look into the thermodynamic features of the material, like how it reacts to changes in temperature and magnetic field. The Monte Carlo models were used to figure out the Curie temperature, which is the point at which the material changes from being ferromagnetic to being paramagnetic. It was also found out how the field affects the relative cooling power, which is a way to measure how well the material works in magnetic refrigeration uses.
The Density Functional Theory (DFT) method is used to make sense of testing results and guess new material features. This lets us model systems that are more or less the same as those we see in the lab. It is worth noting that perovskite oxide has a strong magnetocaloric effect at room temperature. On the other hand, manganese-based perovskites create important connections between their electronic and magnetic qualities. The study of (La, Pr)1−xSrxMnO3 was picked up again. The goal was to show how changing Sr to Pr and La affects the electronic, magnetic, and magnetocaloric features of these manganese-based materials.
The study used two approaches: Monte Carlo models and DFT theory, which helps figure out the values of the Metropolis Monte Carlo algorithm input parameters.
Calculation Details: Density-Functional Theory
and Monte Carlo Simulations
Slater came up with the Augmented Plane Wave method, which is better in the Linearised Augmented Plane Wave (LAPW) method. The LAPW method is used in this part to look into the physical features of matter using density functional theory (DFT) and the WIEN2k code. The gradient generalised approximation (GGA) is used to look at exchange and correlation energy. Kohn-Sham wave functions are made up of spherical harmonic functions inside spheres that don’t meet around atomic sites and Fourier series in the space between the atoms.
For correct results in an acceptable amount of time, you need to use the right input settings. For this method, the muffin-tin sizes you choose depend on the atoms that make up the perovskites you choose. The border between two areas of space, where potentials and wave functions are built in different ways, is shown by the muffintin radius. It takes −6.0 and −9.0 Ry to separate the valence and core states of La0.75Sr0.25MnO3 and Pr0.65Sr0.35MnO3, respectively.
For the Monte Carlo simulations, the Metropolis algorithm is used. This algorithm gives the network circular border conditions. The spin flip is picked based on the difference in energy between the spin being looked at and its neighbours. That’s H = − ∑ Jij Si Sj − H ∑ i Si, where Si and Sj are the spins at lattice site i and site j, respectively. Either way, Mn3+ has a spin moment of S = 2.
In terms of the PSMO, the mean field theory gives us J1 = +42.0 (K), J2 = +39.0 (K), and J3 = +36.0 (K). The DFT method is used to figure out the magnetic links of LSMO by adding up the energies of the ferromagnetic and antiferromagnetic states. When the magnetic coupling constant is positive or negative, it means that there is an antiferromagnetic ferromagnetic contact.
When you add up all the spins, you get M, which is equal to the sum of the internal energies of all the sites. You can find the magnetic entropy by S(T, h) = ∫ T0 Cm T’dT ‘. The magnetic contribution to the susceptibility is given by χ = N kB T[▨M2▩ − ▨M▩].
Crystal Structure of Manganite Perovskite
The precise order of atoms in a crystal is called its crystal structure. Molecular structure, on the other hand, is made up of molecules arranged in a different way. Triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic are the seven crystal forms that can be found in three dimensions. The crystal structure determines the basic qualities of a crystal, which in turn changes the material’s features.
Many of the material’s qualities are controlled by flaws in its crystal structure, like point defects and dislocations. Perovskite oxide, intermetallic, and alloys are some examples of materials that are easy to shape. We have 20 atoms in our material: 4 Pr, 4 Mn, and 12 O. The lattice parameters are a = 5.90 (Å), b = 7.72 (Å), c = 5.52 (Å), and α = β = γ = 90°. A (1 * 1 * 5) supercell with 100 atoms (20 Pr, 20 Mn, and 60 O) is made to match the real-life concentration of Sr (x = 0.35) in the PrMnO3 Pnma lattice.
In the LaMnO3 structure file, replacing one atom of La with Sr makes the compound Pr0.65Sr0.35MnO3, which is the same as the compound that was made in the lab.
Electronic Properties of Manganite Perovskite
Manganite perovskite oxides that are half metallic are very important for spintronics devices and refrigerator magnets. The mechanical, thermal, and dynamic qualities of these materials are all very good. Manganese oxide has twisted octahedral molecular shapes because of the Jan-Teller effect. Oxygen vacancy flaws have a big impact on the electronic and magnetic properties of manganese-based perovskite oxide. When there are oxygen gaps, the valence band features move towards higher binding energies, and the degree of covalency of the Mn bonds goes up.
The overall TDOS and partial PDOS densities of the LSMO and PSMO, along with other electronic features, are looked at. This graph shows the total DOS of Pr0.65Sr0.35MnO3 from -7 to 5 eV as a function of photon energy (eV). It has a gap energy close to the Fermi level for spin down, which means it is half metallic. The fact that the total amount of spin up and down is greater than zero means that the material is ferromagnetic.
The atoms Mn and O make up a big part of the total density around the Fermi level EF. The atom Pr makes up a big part of it from a very low energy level (-0.53 to 0.85 eV). It’s not important for Sr to add to the total DOS near the Fermi level. The 3d orbital describes the Mn atom and the 2p orbital describes the O atom. This means that the Mn-d and O-p atoms hybridise. The half-metallicity and magnetic spin moment are mostly caused by the 2p (O)–3d (Mn) link after this hybridisation.
PDOS of the Mn-d orbitals shows that the dx2−y2 and dxz orbitals are the most common at EF, while the dxy, dyz, and dz2 orbitals are the most common at [−2.36 eV, −1.13 eV]. px, py, and pz spin up in the energy range of -6.8 to -1.11 eV, which is a big part of O-p.
Finally, manganite perovskite oxides that are half-metallic could be used in spintronics devices and cooling magnets.
The study is mostly about how the manganite perovskite substance La0.75Sr0.25MnO3 reacts to magnetism. As a guide, the DOS data around Fermi level EF is used, which shows that the magnetic moments held by the Mn atoms are ferromagnetic. The fact that there is no gap at the Fermi level for spin up shows that the combination is half-metallic. Researchers used ab initio calculations to find the exchange energy, which is given by Eex = (EAFM − EFM). EAFM and EFM are the energies of the Mn atoms that are coupled with antiferromagnetic (AFM) and ferromagnetic (FM) forces, respectively. The DFT method was used to figure out the changes in energy between these magnetic configurations. This proved that the ground state FM is more stable than the AFM states.
The research showed that the system has 100% spin polarisation, with the hybridisation effect determining how strong the spin polarisation is. Near the Fermi EF level, the Mn and O atoms make a big difference in the total density. The Sr and La atoms, on the other hand, make a small difference. The partial values of the orbitals in the valence band showed that the O-2p and Mn-3d orbitals made the biggest contributions. The Sr-5s and La-4d orbitals, on the other hand, made only small ones.
The electric density of Mn-3d comes from the fact that it hybridises with O-2p states. The Griffiths phase in La0.85Ca0.15MnO3 is partly raised into two sub-levels. This happens when the 2p oxygen orbit of MnO6 combines with it. The electronegativity of the system’s elements shows that the half-metallicity and magnetic spin moment are mostly caused by the 2p (O)–3d (Mn) coupling, with the O atom having the largest electronegativity. The magnetic spin moment of Mn is 3.35 µB, which is very close to what scientists have found.
Magnetic and Magnetocaloric Properties of Manganite The study looks at the magnetocaloric effect (MEC) in manganates T1−xSrxMnO3 with (T = La, Pr) and (x = 0.35 and 0.25) by using Monte Carlo models. Using the DFT method, it was found that the two materials being studied are ferromagnetic, which means they can turn into permanent magnets. The manganese element in these products makes them very magnetic.
The magnetocaloric effect (MEC) is a change in a solid’s adiabatic temperature (Tad) or its isothermal variation of magnetic entropy (SM) when it is exposed to an outside magnetic field. Warburg first saw this happen in 1881 when he noticed a rise in temperature when an outside magnetic field was suddenly applied near the Curie temperature of iron. Weiss and Piccard came up with a theory about this effect in 1918 and called it the magnetocaloric effect. In 1926, Debye and Giauque used thermodynamics to explain this effect and argued that it could be used in ways to get to very low temperatures by removing magnetism through adiabatic demagnetisation.
Researchers have found out more about the magnetocaloric features of rare earth manganite. TC = 294 K is the Curie temperature, which is pretty close to what experiments have shown. An ordinary phase change of the second order can be seen in the magnetisation curve at TC (ferromagnetic/paramagnetically).
It is shown that the thermal magnetic entropy change value depends on temperature in a Pr0.65Sr0.35MnO3 material. As the external magnetic field H gets stronger, the Curie temperature stays the same. It agrees well with the experiment in Ref. [31] that the highest value of magnetic entropy is −ΔSmax = 1.98 J K−1 kg−1.
To find TC, ΔSmax, ΔTad, and CP, we used Ref. [31] and Monte Carlo simulations. These are shown in Fig. 2.14 for h = 1 T. The research gives us useful information about how the magnetocaloric effect could be used to make magnetic freezers.
The study is mostly about Manganite Perovskite (Pr0.65Sr0.35MnO3), a molecule that has strong magnetic qualities. There is a transition temperature TC = 294 K where the adiabatic temperature change and heat specific are at their highest. This is supported by the magnetisation curve and the magnetic entropy change curve. The numbers found for ΔTad and CP are similar to what was found in experiments.
Figure 2.15 shows how the relative cooling power (RCP) changes with the magnetic field for Pr0.65Sr0.35MnO3. RCP changes in a straight line with the magnetic field h. For h = 5T, the highest number of RCP is 17557 J/kg. It makes sense that these results came up this way because rare-earth substances with large magnetic moments always have a big magnetocaloric effect and a large RCP maximum.
Figure 2.16 shows how the relative cooling power for Pr0.65Sr0.35MnO3 changes with temperature and different magnetic fields. The highest RCP values rise as the external magnetic field gets stronger. The critical temperature (TC) stays the same, but these RCP values keep going up until they hit their maximum for each magnetic field value.
The magnetic susceptibility changes with temperature when a magnetic field of 0–6 T acts on the compound La0.75Sr0.25MnO3 in the paramagnetic region. This helps us figure out how the compound behaves magnetically. It becomes much less sensitive at its highest point and spreads out over a wider temperature range. For the same reason that TC is moving, the study also sees their highest temperatures moving up at about the same rate.
Different magnetic fields change the specific heat of La0.75Sr0.25MnO3 as a function of temperature. Figure 2.19 shows that as the magnetic field gets stronger, the maximum temperature, which is also known as the Curie temperature, moves steadily towards higher temperatures. But when an outside field acts on something, it makes the highest of the specific heat lower and spread out over a bigger temperature range.
The magnetocaloric effect’s highest value goes up steadily as the magnetic field strength goes up. It peaks at 9.23 J/K kg around TC when the magnetic field changes from 0 to 6 T. It is decided if the combination can be used as a magnetic chiller by comparing its magnetic entropy values to those of other magnetic materials.
Conclusions
The DFT method and the Monte Carlo method are used in this chapter to look at the magnetic, electronic, and magnetocaloric features of perovskites La0.75Sr0.25MnO3 and Pr0.65Sr0.35MnO3. The crystals of both compounds have an orthorhombic shape and belong to the space group Pnma. Their spin polarisation is half metallic, with the Mn spin being magnetically coupled. There is only one change in magnetic properties, from the FM state to the PM state. What TC found was 294 K for PSMO and 310 K for LSMO, which is the same as what the experiments showed. Results for magnetic entropy and specific heat are in line with what was found in experiments. Magnetic entropy is highest at Curie temperature and rises as magnetic field strength increases. It is also found that as the magnetic field gets stronger, the changes in RCP values as a function of temperature and magnetic fields get bigger.
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