Ground state and critical behavior of a core/shell kekulene-like structure by Monte Carlo study
Introduction
Magnetic nanoparticles attracted the attention of researchers due to the interesting changes in the physical and chemical properties after the transition from microparticles [1]. They are of great interest seeing their many promising applications in catalysis [2,3], magnetic resonance imaging [4], magnetic fluids [5], biotechnology [[6], [7], [8]], data storage [9], biomedicine [7,10], and spintronic [11].
The classification of magnetic nanoparticles is based on single (simple nanoparticles) or multiple materials (core/shell and composite particles) [1]. The great functionality of the core/shell nanoparticles is displayed by their properties that can be modified by changing either the core/shell ratio or the constituting material. The utility of magnetic core/shell nanoparticles resides in their magnetic characteristic's tunability, e.g., versatility of performance and overcoming the superparamagnetic limit [12]. More than that, besides the magnetic features already integrated in the core/shell nanoparticles, there is a possibility of adding improved catalytic and optical properties making them more efficient [13]. Recently, an increase in studies on core/shell gold nanoparticles have been noticed. Thanks to their catalytic properties, controlled magnetic and plasmonic properties among other phenomena [14,15], metal-based magnetic core-shell nanoparticles allow great magnetic sensitivity and biocompatibility [16,17].
Theoretically, numerous methods were applied to study the magnetic behavior of the nanomaterials, for instance the mean field theory [18], the density functional theory (DFT) [19], and Monte Carlo simulations [[20], [21], [22], [23], [24], [25]] under the Metropolis algorithm [26]. Our focus is oriented to a core/shell kekulene-like (C48H24) which is a large polycyclic aromatic hydrocarbon (PAH), firstly synthesized by Diederich and Staab [27]. It is constructed by 12 annealed C6 cores organized in the shape of a closed six-membered super-ring [28] (see Fig. 1). Hence, many recent works have studied the bilayer Kekulene structure's magnetic properties with mixed spin-5/2 and spin-2 Ising model [29]. Also studies of the same structure were carried out on a bilayer kekulene-like separated by a nonmagnetic layer with RKKY interactions using Monte Carlo Simulations formed by mixed spin-3/2 and spin-5/2 [30].
As for the study of mixed spin Ising systems, it is due to many reasons: Their relation to potential technological applications such as thermomagnetic recording; Their study enables a better grasp of biometallic molecular systems based magnetic materials; They procure good models to study the ferromagnetic materials; Bounded by certain conditions, they may have a compensation temperature in which the total magnetization disappears under the critical temperature. The great technological importance of these compensation temperature resides in the need of only a small driving field which leads to change the sign of the total magnetization [31]. Among studies of mixed Ising model with both spin-integer ions, the mixed spin-1 and spin-2 Ising system is modestly studied [[32], [33], [34]].
Within this context, the aim of the present research resides in a theoretical investigation of the magnetic properties of the monolayer Kekulene-like structure using Monte Carlo simulations. A thoughtful analysis of the ground states, magnetizations and susceptibilities as a function of the temperature is performed to attain this goal. Also, the effects of the crystal field along with the behavior of the hysteresis loops are discussed.
This paper is organized as follows: Section II is devoted to the Ising model and the Hamiltonian describing this core/shell Kekulene-like structure. Section III deals with the obtained results and their interpretations for the ground state phase diagrams as well as for the Monte Carlo Simulations. Finally, conclusions are given in the last section.
Section snippets
Theoretical model and simulation method
The Ising model used in order to simulate the magnetic properties of the Kekulene-like structure is presented in this section. The Hamiltonian governing the system of a core/shell Kekulene-like, can be written as follow:
In the first three summations, the notations <i,j>, <k,l> and <m,n> indicate the first nearest-neighbor spins. The spins S take the values ± 1, 0, while the spins σ take the values of ±2, ±1 and 0. The
Study of the ground state phase diagrams
To interpret the ground state phase diagrams in various physical parameter planes, we discuss in this sub-section the stable phases according to the Hamiltonian of Eq. (1). The number of total possible phases is 3 × 5 = 15, however, the total number of stable phases found is 13 (see Table 1). In fact, the stable phases correspond to the minimal energies provided by this Hamiltonian. For this purpose, Fig. 2 portray the ground state phase diagrams in the planes: (H, Δ), (H, Jsσ), (H, Jss), (Δ, J
Conclusion
In this work, a study of the magnetic properties and phase diagrams of a core/shell Kekulene-like C48H24 structure consisting of mixed spins (S = 1 and σ = 2), using Monte Carlo simulations have been done. The total number of stable phases found is 13 phases. A perfect symmetry is appearing in the plane (H, Δ) regarding the axis H = 0. For Δ with large and positive values, we found that the phases with higher moments are the more stable ones. The specific phase (0,0) is found to be stable only
Author agreement statement
We the undersigned declare that this manuscript is original, has not been published before and is not currently being considered for publication elsewhere.
We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.
We understand that the Corresponding Author is the sole contact
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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