The study uses Monte Carlo models to look into the magnetocaloric effect on SmFeO3 perovskite that has Mn perovskite added to it. It was found that as Fe ions are replaced by Mn ions, the Néel temperature of the weakly magnetic SmFeO3 drops. As the temperature drops, a change from a paramagnetic to a weak antiferromagnetic state is seen, and as the Mn content rises, so does the Néel temperature. In addition, the study finds a second phase shift, changes in magnetic entropy, and the relative cooling power.
Researchers have looked into how manganite and perovskite ferrite interact magnetically and electrically. Manganites have high magnetocaloric effect values, which makes them a possible material for use in magnetic cooling technology. Experiments have been done to study the magnetocaloric and magnetic features of the SmFe0.5Mn0.5O3 complex perovskite. At 18 K and 234 K, the magnetocaloric effect shows two peaks that are connected to changes in magnetic behaviour. These show the thermal features of SmMnO3 perovskite manganites.
A wide adiabatic temperature range, magnetic entropy change, and high relative cooling power are some of the most important properties for magnetic materials used in magnetic refrigeration technology. Manganite-based products can handle higher temperatures, which is good for the future of technology. Effective field theory was used to study the magnetocaloric features of Ising systems when they are in equilibrium.
The magnetocaloric effect is how magnetic elements change in temperature when the magnetic field is changed. Researchers have looked into the crystal structure and magnetic properties of SmFe0.5Mn0.5O3, a rare earth perovskite single crystal. They used a physical property measurement method to measure the SmFeO3’s DC magnetisation. RFeO3 is a type of rare earth orthoferrite that has interesting physical qualities, such as the ability to change spin and magnetisation when temperature and/or an applied magnetic field are changed.
To study the magnetic properties of the SmFe1-xMnxO3 complex perovskite, Monte Carlo models are used, along with its behaviour in terms of the magnetocaloric effect when the magnetic field changes and x is diluted. For various dilutions and external magnetic fields, the relative cooling power is found. For various dilutions and temperatures, the magnetic coercive field is also found.
Ising Model and Monte Carlo Study
The research is mostly about the lattice characteristics of SmFe0.5Mn0.5O3 perovskite, which is thought to be in unit cells. The total number of spins in the system is N = NSm3+ + NFe3+ + NMn3+. NSm3+, NFe3+, and NMn3+ are the number sites for Sm3+, Fe3+, and Mn3+, respectively. The Hamiltonian of SmFe0.5Mn0.5O3 with Sm3+, Fe3+, and Mn3+ having a ferrimagnetic spin of -5/2, 5/2, and 2 is given below.
H’ = − JSm−Sm ∑, Si Sj − JSm−Fe ∑, Si πk − JSm−Mn ∑, Siqn − JFe−Fe ∑, πkσm − JMn−Fe ∑, πkqn − JMn−Mn ∑
This is qnql – H(∑i Si +∑k πk +∑n qn).
Based on JFe-Fe, JMn-Mn, and x, the exchange interaction JMn-Fe can be written as:
JMn−Fe = 1/4[∑2 m=0^pn(m)(Ji Jj)m/2].
To update the Monte Carlo models, random spins were picked at random and then the states were switched from Si (or πi or qi) to −Si (or −πi or −qi) using Boltzmann’s probability method. There were 105 configurations used in this chapter, and there was at least one Monte Carlo step of time between each one.
This is how you can figure out the magnetic part of SmFe1-xMnxO3’s specific heat:
You can write Cm as β2N(▨E2▩ − ▨E▩ 2), where E = 1 N⟨▨ H’▩ is the site’s internal energy and β = 1 kB T is the absolute temperature. This equation can be used to figure out a material’s magnetic entropy.
¥Tad = −T ¥Sm Cp,H gives you the adiabatic temperature. RC P = ∫ ThTcΦSm(T)dT is the stated measure of relative cooling power (RCP). TN and Th are the cold and hot temperatures that match to the two ends of the half-maximum value of ΦSmaxm.
Results and Discussion: Magnetocaloric Effect
and Magnetic Properties of Perovskite Orthoferrites
A Monte Carlo simulation was used to look into the magnetocaloric effect in SmFe1-xMnxO3 complex perovskite. One is due to Sm3+ and is at 40 K for x = 0.5 and 84 K for x = 0. The other is the anti-ferromagnetic long-range ordering and is at TN = 240 K for x = 0.5 and 400 K for x = 0. We found the critical temperature (TK) and transition temperatures for different amounts of SmFe1-xMnxO3.
As Fe ions are replaced by Mn ions, the critical temperature TK for this weak-antiferromagnetic transition mainly goes down. It’s possible to compare these data to the ones from the experiment. We looked at how TN and TK change with Mn content in SmFe1-xMnxO3 with H = 6 T. We saw that as Mn content goes up, both TN and TK go down. This might be because the sample gets distorted because there are more Mn ions in it.
It changes for SmFe0.5Mn0.5O3 when the external magnetic fields are H = 6, 12, 18, 24, and 30 T. The magnetic entropy changes with temperature. The predicted change in entropy has been seen, which is that the entropy decreases more as the applied field increases. The largest change in magnetic entropy around TN was 3 J. kg1K1 when the temperature was 240 K and the magnetic field was 30 T. We also saw a big change in entropy at low temperatures, when the applied field was changed by 30 T. Also seen is that the decrease in entropy gets bigger as the applied field gets stronger.
In Fig. 8.6, you can see how the relative cooling power (RCP) of SmFe0.5Mn0.5O3 changes with temperature when the field changes. When temperatures go up, the worth of RCP goes up too. As the fraction x goes up, the magnetic coercive field goes up, and as the temperature goes up, it goes down. When the temperature is below TN, the system is antiferromagnetic. When the temperature is above TN, it becomes paramagnetic.
The biggest change in the magnetic entropy for SmFe0.5Mn0.5O3 is shown in Fig. 8.7a and b, which show the magnetic hysteresis cycles for (x = 0.1, 0.5, 0.9, T = 100 K) and (T = 100, 200, 300 K, x = 0.5). The external magnetic fields are H = 6, 12, 18, 24, and 30 T. When the temperature is below TN, the system is antiferromagnetic. When the temperature is above TN, it becomes paramagnetic.
Conclusions
The study uses Monte Carlo analysis to look at the magnetic properties and magnetocaloric effect in the SmFe1-xMnxO3 perovskite. As x goes up, the critical temperature (TK) and the Néel temperature (TN) go down. As the Mn content rises, the paramagnetic weak-antiferromagnetic Néel temperature and spin reorientation drop in a steady way. The highest magnetic entropy goes down as dilution x goes up. The combination is a good choice for magnetic cooling near room temperature because it has a big magnetocaloric effect, a relatively high RCP, a high magnetisation, and is not expensive. The study also shows magnetic hysteresis cycles for different amounts of reduction.
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