Magnetic Properties of a Bi-Layer Borophene Structure with Mixed Spins: Monte Carlo Study
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Magnetic Properties of a Bi‑Layer Borophene Structure with Mixed Spins: Monte Carlo Study M. Qajjour1 · Z. Fadil1 · A. Mhirech1 · B. Kabouchi1 · L. Bahmad1 · W. Ousi Benomar1 Received: 27 April 2020 / Accepted: 26 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Our aim of this work is to study the magnetic properties of a bi-layer borophene structure, using Monte Carlo simulations under the Metropolis algorithm. Such a system is formed by two layers. The first one contains 126 atoms with spin σ = ± 3/2, ± 1/2 and 84 atoms with spins S = ± 1, 0 while the second one contains 84 atoms with spin σ = ± 3/2, ± 1/2 and 126 atoms with spins S = ± 1, 0. We establish, in various planes, the ground-state phase diagrams. Furthermore, we present the thermal variation of the total magnetization and total susceptibility for several values of exchange coupling interactions and crystal field. It is found that the increase in both exchange coupling interactions leads to an almost linear increase in transition temperature in one hand and, on the other hand, to a decrease in the corresponding crystal field transition. Keywords Borophene structure · Monte carlo simulations · Magnetization · Magnetic susceptibility · Critical temperature · Ferrimagnetic exchange coupling interaction
1 Introduction Recently, the scientific community and the majority of researchers in the field of physics of materials are oriented and focused their research on the study of nanomaterials [1–5]. Among these researchers, there are those who are very interested in studying the magnetic properties of the nanomaterials, because they have a major role in different research fields, such as, in the storage of information, in spintronics [6–8] and electric machines [9, 10]. To investigate the theoretical study and simulate these nanomaterials, the researchers have used several approaches and methods such * M. Qajjour [email protected] 1
Laboratoire de la Matière Condensée et Sciences Interdisciplinaires (LaMCScI), Faculty of Sciences, Mohammed V University, P. O. Box 1014, Rabat, Morocco
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Journal of Low Temperature Physics
as the Monte Carlo Simulations (MCS) [11–13], the Effective Field Theory (EFT) [14–16], the Green Functions (GF) [17–20] and the Mean-Field Theory (MFT) [21, 22]. In this paper, to investigate the magnetic properties of the borophene structure, we have used the (MCS), due to its usefulness in investigating the magnetic properties of nanostructure [23]. On another side, the mixed spins in the Ising model are another interesting topic in the study of nanomaterials [24–27], especially the binary (1, 3/2) [28–30]. B. Deviren and Y. Sener [31] have investigated on a core–shell structure, the magnetic properties of mixed spins (1,3/2). They have reported some characteristics phenomena depending on the ratio of the physical parameters in the surface shell and core. They have concluded that this system exhibits exciting critical behaviors such as the first- and second-order
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