Compensation Temperature Behavior in a Nanotube Core-Shell Structure with RKKY Interactions: Monte Carlo Simulations
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Compensation Temperature Behavior in a Nanotube Core-Shell Structure with RKKY Interactions: Monte Carlo Simulations Z. Fadil 1
&
N. Maaouni 1 & A. Mhirech 1 & B. Kabouchi 1 & L. Bahmad 1 & W. Ousi Benomar 1
Received: 13 July 2020 / Accepted: 16 September 2020 / Published online: 23 September 2020 # Sociedade Brasileira de Física 2020
Abstract In this paper, we have studied the magnetic properties of the nanotube core-shell structure with RKKY (Ruderman-KittelKasuya-Yosida) interactions, using Monte Carlo simulations (MCS). The system consists of hexagonal core-shell nanotube structure with mixed spins σ = ± 3/2, ± 1/2 (of the core) and S = ±1, 0 (of the shell), separated by non-magnetic nanotubes. Initially, we start this study by discussing for zero temperature, the ground-state phase diagrams in different planes. Moreover, we investigate for the positive temperature values, the effect of the RKKY interactions on the thermal magnetization and magnetic susceptibility of the system. Additionally, we study the effects of the exchange coupling interactions of the core and of the shell on the compensation and transition temperatures. Finally, we explore the behavior of the magnetic hysteresis cycles as a function of the non-magnetic nanotubes number, the temperature, and the exchange coupling parameters. Keywords Nanotube core-shell structure . Magnetic properties . Compensation temperature . Transition temperature . Monte Carlo simulations . RKKY interactions . Magnetic hysteresis cycles
1 Introduction The carbon element is located on the fourteenth column and the second period of the table of the elements [1, 2]. It therefore has six electrons, which can associate in three different ways called hybridizations. Only sp2 hybridizations and sp3 generate the forms of solid carbons allotropic. In the case of diamonds, carbon is sp3 hybridized and each atom is linked to four other atoms in a tetrahedral arrangement [3, 4]. The four bonds σ give the diamond its hardness, its transparency, and its property of electrical insulation [5]. Graphene has sp2 hybridization where each atom of carbon is linked to three other atoms in a planar pattern hexagonal [6]. In 1985, Smalley and his team highlight another allotropic form of carbon sp2 hybrid: the C60 fullerene or “bucky ball” [7]. These molecules, composed of 60 atoms of carbon, have the rounded shape of a football unlike graphite composed of planes. This new organization of carbon atoms gave rise to the idea that a tubular * Z. Fadil [email protected] 1
Laboratoire de Matière Condensée et Sciences Interdisciplinaires (LaMCScI), Faculty of Sciences, Mohammed V University, P.O.Box 1014, Rabat, Morocco
structure was also possible. It was Iijima in 1991 who was credited with the first observation of this new object called carbon nanotube (CNTs) [8]. The CNTs can be singlewalled carbon (SWCNT) nanotubes having diameters between 0.4 and 6 nm [9–11]. Their lengths range from a few hundred nanometers to several micrometers depending on the methods of s
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