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The spontaneous magnetization in Bohr magneton units as a function of the temperature for a selected value of J ⊥ = 3 K and different values of J // from 1 up to 5 K without any external field. The inset displays details of ∂ ∂ m T curves.
Source publication
In this paper, we investigate the magnetic behavior of a single-walled hexagonal spin-1 Ising nanotube by using the effective field theory (EFT) with correlations and the differential operator technique (DOT). The system consists of six long legs distributed parallel to each other on a hexagonal basis. Within each chain, spin sites are regularly po...
Contexts in source publication
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... magnetization. Figure 2 illustrates the thermal variation of the spontaneous magnetization obtained by solving numerically self-consistent the coupled eqs 7 and 8 for a selected set of positive transverse (J ⊥ = 3 K) and longitudinal exchange constants (J // from 1 up to 5), in the absence of the external magnetic field (h = 0). Note that h is given here in energy units. ...
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... is turned on. This is quite normal since the two exchange constants are positive corresponding to the ferromagnetism, the critical temperature increases with the increase of the exchange constant. Note that the susceptibility peak matches well with the absolute order-parameter derivative |∂M/∂T| obtained from spontaneous magnetization curves (see Fig. 2) elucidating the evidence of a second-phase order ...
Citations
... Some studies explored the magnetic properties of hexagonal Ising nanotube by applying the effective field theory coupled with differential operator technique. These techniques show that some systems with opposite sign of exchange interaction suffer magnetic frustration [21][22][23]. Our interest is to study the magnetic properties and the phase behavior of single walled Ising nanotube (SWINT) influenced by the opposite sign of interaction between the inter-layer and the intra-layer using the Monte Carlo technique. ...
... Depending on such combination of interactions, the system is classified into two kinds: same sign (J 1 > 0; J 2 > 0, and J 1 < 0; J 2 < 0) and opposite sign of interactions (J 1 > 0; J 2 < 0, and J 1 < 0; J 2 > 0). Since some systems with opposite sign of exchange interaction suffers magnetic frustration [21][22][23], this work will pay special attention to the opposite sign of interactions of J 1 and J 2 in SWINT, which arranges spins in A-type and C-type AFM orderings. In A-type, the spin alignment is parallel within the layer and anti-parallel between the layer. ...
The effect of opposite sign of interactions in a single-walled Ising nanotube is investigated using the Wang-Landau algorithm. The thermodynamic observables are calculated from the estimated density of states (DOS) with and without the presence of an external magnetic field. Irrespective of the applied magnetic field, a symmetric trend of DOS is observed for opposite sign of interactions which is in contrast to the asymmetric trend for same sign of interactions. Further, two types of anti-ferromagnetic (AFM) orderings, namely A-type and C-type anti-ferromagnetic order, are observed for opposite sign of interactions. These AFM spin orientations are switched to ferromagnetic (FM) phase by increasing the applied magnetic field ($B$). However, the spin ordering changes from the ordered AFM/FM phase to a disordered paramagnetic phase by increasing the temperature. Phase diagram shows that these three phases coexist around $B=2.0$. This study indicates that, by properly tuning the magnetic properties, the single-walled nanotube can be used for fabrication of new types of magnetic storage nano materials.
... The effective field theory with correlations is used to analyze the phase diagram and magnetization of a cylindrical nanotube as a transverse Ising model [22]. Using the differential operator technique and effective field theory, the magnetic properties of a six-legged spin half and spin one nanotubes are studied in the presence of an applied magnetic field [23,24]. The phase transition and magnetization of Ising nanotubes are analyzed by cellular automata approach with ferromagnetic and anti-ferromagnetic interactions [25]. ...
The Monte Carlo analysis for the magnetic response of a single-walled nanotube using the Metropolis and Wang-Landau algorithms is reported in the present paper. The nanotube architecture used in the present study utilizes the spin half Ising model with nearest neighbors interaction and obtained various magnetic orderings, namely ferromagnetic, G-type anti-ferromagnetic, A-type anti-ferromagnetic, and C-type anti-ferromagnetic. It is also found that the phase changes from ferromagnetic/anti-ferromagnetic to paramagnetic with the modification of system’s control parameters. The transition temperatures is determined for various interaction strength in the absence of magnetic field and for fixed interaction strength with the inclusion of external magnetic field. The present study confirms the transition from ferromagnetic/anti-ferromagnetic to paramagnetic is a second-order transition.
... The effective field theory with correlations is used to analyze the phase diagram and magnetization of a cylindrical nanotube as a transverse Ising model [22]. Using the differential operator technique and effective field theory, the magnetic properties of a six-legged spin half and spin one nanotubes are studied in the presence of an applied magnetic field [23,24]. The phase transition and magnetization of Ising nanotubes are analyzed by cellular automata approach with ferromagnetic and anti-ferromagnetic interactions [25]. ...
We present the Monte-Carlo analysis report for the magnetic response of the single-walled nanotube using the Metropolis and Wang Landau algorithms. Our nanotube architecture uses the spin half Ising model with nearest neighbors interaction. We find the phase changes from ferromagnetic/anti ferromagnetic to paramagnetic by modifying the system interaction parameters. We determine the transition temperatures for varying interaction strength in the absence of the magnetic field. We find the transition temperature changes with the external magnetic field for a fixed interaction strength. Our study confirmed that the transition from ferromagnetic/anti ferromagnetic to paramagnetic is second order.
... Magnetic properties of a transverse Ising nanotube with a core-shell structure are also investigated for different cases [16]. By utilizing the EFT with correlations within differential operator technique (DOT), Z. Elmaddahi et al. investigated the magnetic behavior of single-walled hexagonal spin-1 Ising nanotube where interesting phenomena were highlighted, in particular for competitive exchange couplings where magnetization plateaus and frustration are found [17]. In other words, the authors have examined the impact of the applied field and temperature on the magnetic properties counting the magnetization, the susceptibility, the specific heat, and the thermal energy of the ferromagnetic and the antiferromagnetic cylindrical mixed spin 1 shell and spin ½ center Ising nanotube by utilizing the EFT [18]. ...
The effective field theory with correlations has been employed to study the hysteresis behavior of a ferromagnetic and ferrimagnetic three-walled mixed-spin Ising nanotube with an inner hexagonal vacancy. The effects of different exchange couplings, single-ion anisotropies, and temperature on the hysteresis loops of the sublattices and the overall system are attentively discussed. Multiple hysteresis loops have been observed in the system under certain physical hamiltonian parameters. It is found that the remanences and the coercivity of the sublattices and the system are strongly affected by the temperature, the exchange couplings, and the anisotropy. A satisfactory agreement can be qualitatively achieved by comparing our results with experiments and theoretical studies. Amazing behaviors are revealed thanks to the geometry, the different spins, and the multiple interactions involved in the system.
Highlights
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A three-walled mixed-spin (½, 1, ½) nanotube is constructed.
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Different magnetic properties for ferromagnetic and ferrimagnetic cases are established.
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Temperature, exchange couplings, and anisotropy have a strong effect on the magnetization plateaus and the multiple-loop hysteresis cycles.
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Original behaviors are revealed.
Journal of Magnetism and Magnetic Materials
Volume 523, 1 April 2021, 167565
https://doi.org/10.1016/j.jmmm.2020.167565
... Beyond the variety of hysteresis loop forms, it is interesting to note that there are many intermediate steps in the hysteresis cycle. It is generally known that such magnetic systems with conflicting couplings can display plateaus-like behavior within the hysteresis cycle, especially at low temperatures [47]. ...
The magnetization loops of a hexagonal spin-3/2 Ising nanotube are examined in the framework of the effective field theory with correlations, based on the differential operator technique. We have explored the impacts of distinctive exchange couplings on key physical parameters such as Phase diagram, magnetization, susceptibility, internal energy, and specific heat. Some special phenomena are inspected in terms of thermal effects or crystal-field when the other inherent parameters of the nanotube are adjusted. Furthermore, We have found that the exchange couplings, the temperature, and single-ion anisotropy have a strong impact on the shape and the number of hysteresis loops as well as on the coercive field and magnetization behaviors.
Keywords :
Spin-3/2 Ising nanotubeExchange interactionsSingle-ion anisotropyHysteresis loopsEffective field theoryPhase diagramMagnetization plateaus
Thermal fluctuations in magnetizations and magnetic phase diagrams of a diatomic molecule are investigated on the Bethe lattice (BL) with coordination number $$q=3$$ q = 3 by using the exact recursion relations (ERR). Each molecule is assumed to interact with others via its atoms in terms of various bilinear interaction parameters. They involve the interaction of atoms within each molecule as well as the interaction of atoms between the molecules. Each site is also considered to have an active crystal field. Following the determination of the average magnetization of the molecule and its atoms in the central molecule of the BL in terms of ERR, their thermal fluctuations and potential phase diagrams are thoroughly analyzed. Numerous phase regions, ordered (O), i.e., ferromagnetic (FM) or antiferromagnetic (AFM), paramagnetic (P), and random (R), are discovered. The phase boundaries between these phases are obtained in terms of first- and second-order and random phase transition lines. Therefore, various critical phenomena, including tricritical point (TCP), bicritical point (BCP), critical end point (CEP) and reentrant behavior (RB), are observed.
"The magnetic properties and phase diagrams of a hexagonal nanotube with core-shell structure have been examined within the framework of the mean field theory based on the Bogoliubov inequality as well as the Monte Carlo simulation via the Metropolis algorithm. We have studied in detail the influences of the different ex- change couplings and the crystal field on the phase diagrams of the system. This study allowed us to discover the existence of interesting critical phenomena, in particular the compensation behavior. Moreover, we have investigated the behavior of the magne- tizations corresponding to each of the phase diagrams in order to verify the obtained results."
The effect of opposite sign of interactions in a single-walled Ising nanotube is investigated using the Wang–Landau algorithm. The thermodynamic observables are calculated from the estimated density of states (DOS) with and without the presence of an external magnetic field. Irrespective of the applied magnetic field, a symmetric trend of DOS is observed for opposite sign of interactions which is in contrast to the asymmetric trend for same sign of interactions. Further, two types of antiferromagnetic (AFM) orderings, namely A-type and C-type antiferromagnetic order, are observed for opposite sign of interactions. These AFM spin orientations are switched to ferromagnetic (FM) phase by increasing the applied magnetic field (B). However, the spin ordering changes from the ordered AFM/FM phase to a disordered paramagnetic phase by increasing the temperature. Phase diagram shows that these three phases coexist around \(B=2.0\). This study indicates that, by properly tuning the magnetic properties, the single-walled nanotube can be used for fabrication of new types of magnetic storage nanomaterials.
Using the Effective Field Theory with correlation, we investigate the magnetic properties and the phase diagram of a mixed-spin (1⁄2, 1, 1⁄2, 1) Ising core-multi shell nanowire structure. Typical temperature dependence of the total magnetization, the core and shell magnetization for several fixed values of exchange couplings were discussed in detail. The phase diagrams of the critical and compensation temperatures were displayed in various Hamiltonian parameter planes. Our established results have been successfully compared with results from several experimental and theoretical studies. The ultimate objective is to stimulate research into the
design and development of innovative nanomaterials for targeted applications.
The present work clarifies a failure of the effective-field theory in predicting a false spontaneous long-range order and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires with either zero- or one-dimensional magnetic dimensionality. It is conjectured that the standard formulation of the effective-field theory due to Honmura and Kaneyoshi generally predicts for the Ising spin systems a spurious spontaneous long-range order with nonzero critical temperature regardless of their magnetic dimensionality whenever at least one Ising spin has coordination number greater than two. The failure of the effective-field theory is exemplified on a few paradigmatic exactly solved examples of zero- and one-dimensional Ising nanosystems: star, cube, decorated hexagon, star of David, branched chain, sawtooth chain, two-leg and hexagonal ladders. The presented exact solutions illustrate eligibility of a few rigorous analytical methods for exact treatment of the Ising nanosystems: exact enumeration, graph-theoretical approach, transfer-matrix method and decoration-iteration transformation. The paper also provides a substantial survey of the scientific literature, in which the effective-field theory led to a false prediction of the spontaneous long-range ordering and phase transition.
