A Monte Carlo study of the yttrium-based Heusler alloys: Y 2 CrGa and YFeCrGa Samira Idrissi Mohammed V University of Rabat, Rabat, Morocco Soumia Ziti Computer Science, Faculty of Sciences, Mohammed V University of Rabat, Rabat, Morocco Hicham Labrim DERS, CNESTEN, Rabat, Morocco, and Lahoucine Bahmad Mohammed V University of Rabat, Rabat, Morocco Abstract Purpose – In this paper, using Monte Carlo simulations (MCSs) under the metropolis algorithm, the authors study the magnetic properties of the yttrium-based Heusler alloys: Y 2 CrGa 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 Y 2 CrGa 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 Y 2 CrGa by a Hamiltonian containing only one magnetic spin moment (S 5 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q 5 5/2 and s 5 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: Y 2 CrGa and YFeCrGa. Design/methodology/approach – In this paper, the authors study the magnetic properties and the critical behavior of the yttrium-based Heusler alloys, Y 2 CrGa 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 5 0). On the other hand, for non-null temperature (T ≠ 0), the authors investigate the critical behavior of these two yttrium-based Heusler alloys: Y 2 CrGa and YFeCrGa. It is worth to note that the full-Heusler alloy Y 2 CrGa contains only one magnetic atom (Cr), while the quaternary Heusler alloy YFeCrGa has two magnetic atoms (Cr and Fe). Hence, the compound Y 2 CrGa can be modeled by a Hamiltonian containing only one magnetic spin moment (S 5 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q 5 5/2 and s 5 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: Y 2 CrGa and YFeCrGa. Findings – The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y 2 CrGa 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 Y 2 CrGa by a Hamiltonian containing only one magnetic spin moment (S 5 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q 5 5/2 and s 5 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: Y 2 CrGa and YFeCrGa. Research limitations/implications – The authors elaborate the ground-state phase diagrams of the more stable configurations. It is worth to note that the full-Heusler alloy Y 2 CrGa 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 Y 2 CrGa by a Hamiltonian containing only one magnetic spin moment (S 5 2), while the quaternary Heusler alloy YFeCrGa is modeled by a Hamiltonian containing two magnetic spin moments (Q 5 5/2 and s 5 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: Y 2 CrGa and YFeCrGa. Yttrium-based Heusler alloys The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/1573-6105.htm Received 5 September 2020 Revised 4 November 2020 Accepted 28 November 2020 Multidiscipline Modeling in Materials and Structures © Emerald Publishing Limited 1573-6105 DOI 10.1108/MMMS-09-2020-0221