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In this paper, using Monte Carlo simulations (MCSs) under the metropolis algorithm, the authors study the magnetic properties of the yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa. In the first step, the authors elaborate and discuss the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y₂CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

In this paper, the authors study the magnetic properties and the critical behavior of the yttrium-based Heusler alloys, Y₂CrGa and YFeCrGa, using MCSs under the metropolis algorithm. In the first step, the authors elaborate and discuss the ground-state phase diagrams of the more stable configurations for the both structures at null temperature (T = 0). On the other hand, for non-null temperature (T ≠ 0), the authors investigate the critical behavior of these two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). Hence, the compound Y₂CrGa can be modeled by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). Moreover, the results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y₂CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y₂CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y₂CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y2CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y₂CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). This leads to modeling of the compound Y₂CrGa by a Hamiltonian containing only one magnetic spin moment (S = 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q = 5/2 and s = 2). The results of the study reveal that the critical temperature increases when increasing the reduced crystal field for the two studied compounds. To complete this study, the authors elaborated the hysteresis cycles of the two yttrium-based Heusler alloys: Y₂CrGa and YFeCrGa.

The purpose of this paper is to investigate the magnetic properties and the ground state phase diagrams of the double perovskite La₂NiMnO₆ using the Monte Carlo simulations (MCS).

In this work, the authors propose a Hamiltonian modeling this compound, described by an Ising model, with different exchange coupling interactions J11, J12 and J22 between the only magnetic atoms Ni and Mn.

Starting with the ground state phase diagrams, the authors present and discuss the stable configurations in different physical parameter planes. On the other hand, the authors present the investigation of the magnetic properties and the magnetization behaviors of the magnetic susceptibilities, as a function of temperature, crystal field, the exchange coupling interactions and the Zeeman energy. To complete this study, the authors illustrate the dependency of the total magnetizations for the hysteresis loops of the double perovskite La₂NiMnO₆ compound. This study is done for fixed values of temperature, the exchange coupling interactions and crystal field.

The authors modeled the different physical parameters of the double perovskite La₂NiMnO with a Hamiltonian describing the system. At T=0K, the authors discussed the ground state phase diagrams of different physical parameters planes. For non-null temperature values, the authors studied the magnetic behavior of the double perovskite La₂NiMnO using MCS under the metropolis algorithm. The authors expect that the results of these simulations can provide some important keys for the experimental research and technology applications of the double perovskite La₂NiMnO₆ in the future.