The study looked at the magnetocaloric, electronic, and magnetic features of perovskite oxide Ba1-xSrxFeO3 with x values between 0 and 0.2 using density functional theory (DFT) and Monte Carlo simulations. Some of the computer methods used were spin polarisation and modified Becke-Johnson potential. This study gives us a full picture of Ba1-xSrxFeO3, showing how the Sr swap changes things and giving us ideas for possible uses.
Fe-based perovskite oxides, whose chemical formula is AFeO3, are very useful because their crystal structures are flexible and they contain A-Fe ionic groups. The charge change of Fe4+ ions and the spiral spin structure of these molecules are very important to their physical features. By adding non-magnetic elements to AFeO3, these qualities can be changed to fit different uses. This makes it possible to make perovskite oxide materials that can do more than one thing. The study is mostly about BaFeO3 and Ba0.8Sr0.2FeO3. These materials have been looked at both theoretically and physically to find out their magnetic, magnetocaloric, dielectric, and optical qualities. When it comes to controlling the magnetocaloric effect, high ionic and electronic conductivities, and chemical stability in reducing atmospheres, the Sr replacement Ba is very important.
Density-Functional Theory and Monte Carlo
Simulations
The research is mostly about the electron exchange-correlation energy of the Fe-3d states in the FeO3 molecule. The calculations were done using DFT and DFI + U calculations, which were reproduced in the Wien2k computer code. The generalised gradient approximation (GGA), GGA + U, and TB-mBJ approximations were used to look at the electron exchange–correlation energy. The TB-mBJ approximation gives exact values for the gap and magnetic moment, while the GGA + U approximation adds some exchange to orbitals with a certain rotational character (d or f).
Tran and Blaha came up with the Modified Becke–Johnson (mBJ) formula, which looks like this: The equation for UmB J is: cU BR χ,π (r) + (3c – 2) 1 π √ 5 12 √ 2tπ (r) ρπ (r). It’s written with an index π. How the number U is chosen is an important part of the GGA + U method. A number of different U values between 4 and 6 eV have been offered.
Monte Carlo models (MCS) are a good way to study magnetic qualities and how they work. They are based on the Metropolis method, which lets Boltzmann statistics be set up in a variety of ways. The normalised Boltzmann factor that shows how likely it is that formation x will show up at thermal equilibrium is: P = 1 Z exp(−H’ kB T), where Z is the system’s partition function and H’ is its Hamiltonian.
It looks like this is how the Hamiltonians of BaFeO3 and Ba0.8Sr0.2FeO3 are written: H’ = − ∑
Shij Si Sj – H ∑i Si, where Si and Sj are the spins at site i and site j of the lattice. For x = 0, Fe’s spin moment is S = 2. For x = 0.2, it is S = 3/2.
The exchange energy is used to figure out the exchange pairs Jij. What makes something magnetic is its internal energy E = 1 N ▨H▩ and its magnetisation M = 1 N ∑i πiλ. [24] goes into more depth about these traits.
Crystal Structure of Ferrite Perovskite
Once BaFeO3 crystallises, it does so in the cubic Pm3m space group, where a = b = c = 4.012 (Å) and α = β = γ = 90°. Four equal Ba atoms are joined together to make six equal BaO12 cuboctahedra. These cuboctahedra share corners with twelve equal BaO12 cuboctahedra, faces with six equal BaO12 cuboctahedra, and faces with eight similar FeO6 octahedra. All of the Ba–O bonds are 2.85 Å long.
To get a reasonable amount of Sr (x = 0.2) in the cubic structure of BaFeO3, a supercell (1 × 1 × 5) was made with 25 atoms (5 Ba, 5 Fe, and 15 O). A Sr/Ba swap in the supercell of the 5 Ba total atom leads to a composition of Ba0.8Sr0.2FeO3, which is the same as the makeup that was made in the lab.
The picture (3.3a) displays two different Ba sites. The first site is made up of four identical SrO12 cuboctahedra, eight BaO12 cuboctahedra in the corners, a SrO12 cuboctahedron on the face, five BaO12 cuboctahedra on the face, and eight FeO6 octahedra on the face. There are six equivalent BaO12 cuboctahedra at the second site. There are also four equivalent BaO12 cuboctahedra on the faces and four equivalent SrO12 cuboctahedra on the faces.
Three different Fe sites can be seen in Fig. 3.3b. The first Fe site makes FeO6 octahedra with six equivalent FeO6 octahedra, faces with four equivalent BaO12 cuboctahedra, and faces with four equivalent SrO12 cuboctahedra. The shared corners of an octahedron are not curved.
Electronic Properties of Ferrite Perovskite
The study is mostly about the total density of state (DOS) for Ba1-xSrxFeO3 as a function of the energy ranged from -8 to 3.5 eV. This was found using the GGA model. The ferromagnetic order of both substances is the same at the ground state, with BaFeO3 being half-metallic. This matches up well with both theory and experimental results. Ba0.8Sr0.2FeO3, on the other hand, is very close to half-metallicity.
The GGA method is usually not taken into account fully, which means we need to find a more accurate method or fix the gap that was measured. To study the crystal structures of Ba0.8Sr0.2FeO3, the mBJ method is used as a first correction, and the GGA + U method is used as a second correction.
At the Fermi level, the total DOS profiles for the GGA + U and TB-mBJ approximations are very similar. At the Fermi level, both profiles show 100% spin polarisation. It is also seen that half of the metals cause this strong polarisation. The total density near the Fermi level is largely made up of Fe-3d and O-2p atoms, which shows that there is a lot of hybridisation between the O-2p and Fe-3d orbitals. This means that the 2p(O)-3d(Fe) link is probably the main reason why BaFeO3 is half-metallic.
The Fe d orbital is split into t2g states that are eg doubly degenerate and triply degenerate. Between the Fe-eg and O-p states, there is strong hybridisation (Figure 3.2), but only weak hybridisation between the Fe-t2g and O-p states. The 2p(O)-3d(Fe) link is what makes the connection between the Fe-eg and O-p states so strong.
The GGA + U method, the TB-mBJ method, and the EF method are all used to study the electrical features of Ferrite Perovskites. As x ranges from 0 to 0.2, the GGA model, TB-mBJ, and EF methods are used to compare the total and partial densities of states of Ba1-xSrxFeO3.
In addition to looking into the electronic and magnetic properties of Ferrite Perovskites, the study also looks into their ferromagnetic order and magnetic properties. The findings suggest that BaFeO3’s half-metallicity is mostly caused by the 2p(O)-3d(Fe) coupling, with the Fe d orbital being split into two sets of two degenerate electrons and three sets of three degenerate electrons.
Magnetic and Magnetocaloric Properties of Ferrite
Perovskites
The study used Monte Carlo models to find out what the magnetic qualities and magnetocaloric effect of Ba1-xSrxFeO3 were. The DFT method was used to figure out the nearest, next-nearest, and next-next neighbours trade contacts. The findings showed that Jij values went down when 0.2 wt.% BaFeO3 was added. This was because the energy difference ΔE and the magnetic spin moment both went down.
Researchers looked at the magnetic and electronic features of Fe by using U and TBmBJ. This caused the total magnetic moment and the moment magnetic to go up. We found the magnetic spin moment of iron in BaFeO3 by using the mBJ potential along with the GGA-PBE approximation and the GGA + U approximation for Ba1-xSrxFeO3. We found the magnetic spin moment of iron in Ba0.8Sr0.2FeO3 using GGA + U with U = 4 eV, U = 5 eV, and U = 6 eV. We also found the magnetic spin moment of iron in Ba0.8Sr0.2FeO3 using the TB-mBJ model.
When Sr is switched out for Ba, the magnetic moment value goes down. K. Yoshii has done experiments that show this to be true. The magnetisation of BaFeO3 changed from a ferromagnetic state (FM) to a paramagnetic state (PM) as the temperature increased in a magnetic field of H = 1, 3, and 5T. This happened close to the Curie temperature (TC). There was a comparison between the total magnetic moment found using GGA, GGA + U, and the TB-mBJ method and results from experiments and other theories.
Even though the critical temperature Tc stayed the same, the highest susceptibility and the specific heat both went down a lot as the magnetic field got stronger. Concerning the replacement Sr, the maximum of both the sensitivity and the specific heat went down when 0.2 concentrations of Sr were added to Ba.
It was seen that the reciprocal change in magnetic entropy as a function of temperature in different magnetic fields applied to Ba1-xSrxFeO3 got bigger as the magnetic field got stronger. The Sm (T) curves got steeper as the temperature dropped below the Curie temperature and reached their highest points when T = TC. When x = 0 and x = 0.2, the Sr swap made the highest number of –ΔSm (T) go down.
As a result, the study found that adding Sr instead of Ba lowers the magnetic moment value, which is in line with what was found in experiments. The study also shows how important it is to think about the magnetic qualities of materials and how they might be used in different areas.
Conclusions
This part talks about the basic theories, Monte Carlo and ab initio methods, and techniques used to figure out the electronic and magnetic features of BaFeO3 materials. The GGA method was used to figure out the electronic and magnetic properties, but the results were not as accurate as the actual ones because the exchange correlation term was not known. Different types of corrections, like GGA + U and TBmBJ, were used to make things more accurate.
Even though TB-mBJ worked on both magnetic and non-magnetic materials, it did not work on magnetic materials. With the GGA + U estimate, bands, total moment, and fixed load could all be located. Both methods were used to fix problems and get results that were very close to what the experiments showed.
The main goal of this chapter was to look at how the element Sr changes the electronic, magnetic, and magnetocaloric qualities of compounds made of BaFeO3. It was found that the system Ba1-xSrxFeO3 is half metallic and ferromagnetic by looking at its total and partial DOS and difference energy values. The magnetic moment and Curie temperature went down when Sr was substituted. Researchers used Monte Carlo models to look into magnetic qualities like specific heat, magnetisation, magnetic entropy, and susceptibility. We saw that the Ba0.8Sr0.2FeO3 material changed into a second-order PM-FM phase around 53 K. It had a high magnetic entropy for x = 0.2 at 5T.
The findings showed that BFSO has good magnetic qualities that meet the needs of devices that use magnets and spintronics.
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