The chromite structure is ACrO3 perovskite, and A is a rare earth chromite that has magnetoelectric multiferroics living together. Because of these features, it can be used in a lot of different technologies, especially in optical, spintronic, and thermoelectric ones. Some of these uses are storing information, making electrical parts, and making spintronic devices. Below a certain temperature called the Néel temperature, chromite-based materials are usually antiferromagnetic (AFM), and above that temperature, they are paramagnetic (PM). This chapter shows the outcomes of studies that used density functional theory and Monte Carlo modelling to look at the GdCrO3 system’s electronic, optical, thermoelectric, magnetic, and magnetic features. The density functional theory is used to study the structure of electrons, and the Monte Carlo simulation is used to study the magnetocaloric effect.
Calculation Methods
Density Functional Theory
The study used the density functional theory (DFT) method in WIEN2k to figure out GdCrO3’s electronic and optical features. The generalised gradient approximation (GGA) parametrised by Perdew, Burke, and Ernzerhof was used to figure out the exchange-correlation potential. In the first step, you had to list some important factors that affect how long the estimate takes and how accurate it is. The ball sizes from the muffin tin RMT spheres were used, and the Monkhorst–Pack method was used to figure out the number of k points in the first Brillouin zone. The cutoff energy was picked to make sure that the total energy ET would meet. It was when the gap was less than 1 mRy that the charge converged. It was the average of the biggest wave vector that was used for the creation of the charge density’s plane waves that Gmax = 12. For better convergence, 1000 k points in the irreducible BZ were used to look at visual features. Using the tool BoltzTraP, the electrical structure was used to get the thermoelectric properties. The total energy was found using self-consistent formulas, which made it possible to find out what GdCrO3’s physical qualities are. The DFT calculations were done at room temperature, but the Ising model was used to get an idea of the Neel temperature for materials that are not magnetic.
Monte Carlo Study
Four sums are used to find the Hamiltonian of the mixed-spin Ising model of GdCrO3. These are the first, second, third, and fourth sums. The first sum is about how spins next to each other interact, and the fourth sum is about the energy that comes from an outside magnetic field. The Hamiltonian function only has negative signs (−) on its terms, which lets it be categorised by the sign of the exchange coupling.
The Ising model is called ferromagnetic if most of its nearest neighbour spins are in a configuration where their polarisation directions are the same and antiferromagnetic if most of them are in a configuration where their polarisation directions are opposite to each other. The second part of the Hamiltonian shows how the magnetic field outside of a spin reacts with it.
In the structure, there are NGd = 2210 Gd atoms and NCr = 2420 Cr atoms. To use Monte Carlo modelling to find the critical temperature, the difference energy ΔE is used to figure out the coupling constants JGdGd, JCrGd, and JCrCr.
Here’s how to describe GdCrO3’s magnetic properties:
The energy inside each site is E = 1 N ▨H▩, the magnetic field is MS = 1 Ns ▨∑i Si▩, and the total magnetic field of GdCrO3 is MT = Ns MS + Nπ Mπ Ns + Nπ. A magnetic susceptibility is given by χS = β(▨M2 S ▩−▨MS▩) and χπ = β(▨M2 π ▩−▨Mπ ▩). The total magnetic susceptibility is given by χT otal = NsχS + Nπχπ Ns + Nπ.
The entropy change caused by the magnetic field is given by ΥS(T, h) = ∫ h0(∂ M∂T) h dh. The RCP is given by RC P = ∫ Th TC ΦS(T) dT.
Crystal Structure of Perovskite Chromites
GdCrO3 is a chemical that crystallises in the shape of an orthorhombic square with a Pnma space group. There are 12 oxygen atoms, 4 chromite atoms, and 4 gadolinium atoms in the unit cell. That’s a = 5.301 (Å), b = 5.533 (Å), c = 7.599 (Å), and α = β = γ = 90° for GdCrO3. Gd3+ is connected to eight O2− atoms in an eight-coordinate shape. On the other hand, Cr3+ is connected to six O2− atoms to make CrO6 octahedra that share corners. There are two different O2− sites, and O2− is connected to three identical Gd3+ atoms and two identical Cr3+ atoms in a five-coordinate shape. Two equivalent Gd3+ and two equivalent Cr3+ atoms are bound to O2− in the second O2− site. This makes a twisted OGd2Cr2 tetrahedron with four corners that share one edge.
Electronic Properties of Perovskite Chromites
The study is mostly about figuring out the band structures of GdCrO3, which has a band gap of 1.26 eV. In the first Brillouin zone, the energy gaps are found along lines with a lot of uniformity. The valence band’s highest point and the conduction band’s lowest point are both at the same point in the band structures. This means that GdCrO3 is a straight gap semiconductor with a band gap of 1.26 eV. To figure out how the energy of electrons in the valence and conduction bands is spread out, the electronic density of states (DOS) is very important. The GGA-PBE approach is used to get the total and partial frequencies of states. The fact that TDOS is symmetrical with respect to the energy axis proves that the total magnetic moment is 0 μB. This means that GdCrO3 is an antiferromagnetic (G-AFM) type. The PDOS talk shows that the O-p and Cr-d orbitals around fermi and the Gd-f and O-p in [−4, −2] make a big difference in terms of electrons. The energy difference ΔE = (EAFM − EFM) is found to be greater for AFM than for FM in the ground state.
Dielectric and Optical Properties of Perovskite
Chromites
This part talks about GdCrO3’s visual qualities, such as its ability to absorb light and return it. If you write the dielectric frequency function in this way, it shows the optical properties:
There is an imaginary part of the dielectric function called ε2(ω), which is equal to ε1(ω) plus i. You can get the imaginary part of the dielectric function, ε1(1), which is equal to 1 plus π, and use it to find the real part of the function.
The points you see on the real and imaginary parts of the dielectric function’s spectrum are caused by the change from the valence band to the conduction band. The main reason for these peaks in our molecules is that electrons from the O-2p, Gd-f, and Cr-3d states move from the valence bands to the Gd-f and Cr-d states of the conduction bands.
The most important thing in optical math is the optical absorption α(ω). It’s also the easiest way to figure out the bandgap and band structure of both crystalline and non-crystalline materials. The absorption of GdCrO3 is shown in Fig. 4.7a. The main absorption edge and a number of peaks match to the direct – – transition. It mostly moves from the filled state of the valence band (VB) Cr-d, O-p to the Gd-f and Cr-d states between 1.30 eV and 4 eV.
The range of reflectivity R(ω) for a normal incidence on the surface of a crystal can be found by using the equation R(w) = √ε(w) – 1 and √ε(w) – 1. This shows that these substances have a high reflectivity at low energies, starting at 0.181%.
Thermoelectric Properties of Perovskite Chromites
The Seebeck value tells you how well a thermocouple works. GdCrO3 has a Seebeck coefficient that goes down with temperature and peaks at 8.75 × 10–6 V/K for both spin up and spin down. The electrical conductivity response goes up as the temperature goes up, reaching a high point of 4.90 * 1014 W K−1 m−1 s−1 for both spin up and spin dn. In GdCrO3, the conductance goes up with temperature and peaks at 2.55 * 1019 (Ω−1 cm−1 s−1) for spin dn and 2.54 * 1019 (Ω−1 cm−1 s−1) for spin up. Even the thermal conductivity goes up with temperature. For spin up and spin dn, it reaches a high point of 4.90 * 1014 W K−1 m−1 s−1.
Magnetic and Magnetocaloric Effect of Perovskite
Chromites
Because they behave in a lot of different ways and help us understand the basic features of matter, magnetic materials are very important to technology. We are looking at how magnetic and magnetocaloric GdCrO3 is in this work. Monte Carlo models are used to figure out the magnetic qualities and magnetocaloric effect based on the overall magnetic moment of Cr and Gd. It was found that the Neel temperature is 176 K, which is the same as what was found experimentally.
The magnetisation curve displays a standard phase change of the second order at T N (antiferromagnetic/paramagnetic), with clear spin reorientation changes in this substance. The temperature at which the spin reorientation happens is found to be TSR = 78 K. There is a peak in a lower area that may be responsible for the long-range spin reorientation of the Fe3+ sublattice.
We used Monte Carlo simulations to find out how the temperature magnetic entropy of GdCrO3 changes. At 5 T, the highest number we got was −ΔS = 2.64 J · K−1 · kg−1. There is a straight line relationship between the magnetic field h and the relative cooling power (RCP). The highest value of 25 J/kg is found when h = 5 T.
It is shown how the relative cooling power changes with temperature for a number of magnetic fields. The values go up as the magnetic field strength and temperature go up until they hit saturation for each magnetic field strength. The magnetic hysteresis cycle for different temperatures is also shown. This shows that as the temperature rises, the magnetic coercive field and remanent magnetisation drop until they reach zero above the transition temperature. At temperatures higher than the transition point, the system acts in a superparmagnetic way.
Conclusions
The main goal of the study is to find new materials that have many useful qualities. The study looked at the electronic, magnetic, thermoelectric, and magnetic features of perovskite GdCrO3 using the FP-LAPW method and the density functional theory (DFT). GdCrO3 was found to be a semiconductor with a straight gap in its band structure by the study. For example, the dielectric function, the absorption coefficient, and the reflection spectrum were some of the optical features that were looked at in more detail. The BoltzTraP code was used to test the thermoelectric reaction, and the Monte Carlo simulation was used to find the Néel and spin reorientation temperatures. The data can be used to plan future experiments and make predictions. The highest value of magnetic entropy goes up as the external magnetic field goes up, but hC and Mr numbers go down as the temperature goes up.
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