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Solid State Communications

Magnetic properties of spin- 72 Blume-Capel chain under a magnetic field

Mounirou Karimou, Mehmet Batı

Published Nov 18, 2020• 6 citations
Publisher

Abstract

A magnetic property of the one dimensional spin-7/2 Blume-Capel model under the magnetic field has been investigated by means of transfer matrix method. Thermodynamic response functions are also obtained for varying values of reduced thermodynamic temperature and scaling magnetic field. We have seen that the crystal field strongly affects magnetic plateau mechanism. Our simulation results demonstrate that the plateau becomes smoother when the value of the temperature increased. Entropy of the system goes to zero rapidly for positive crystal field values so we see only saturation values of the system. We observed that the minimum of specific heat tends to shift to the relatively lower thermodynamic temperature regions as the strength of the crystal field is increased.

DOI
10.1016/j.ssc.2020.114137

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•Aug 9, 2019•0 citations
A magnetic property of the one dimensional spin-7/2 Blume-Capel model under the magnetic field has been investigated by means of transfer matrix method. Thermodynamic response functions are also obtained for varying values of reduced thermodynamic temperature and scaling magnetic field. We have seen that the crystal field strongly affects magnetic plateau mechanism. Our simulation results demonstrate that the plateau becomes smoother when the value of the temperature increased. Entropy of the system goes to zero rapidly for positive crystal field values so we see only saturation values of the system. We observed that the minimum of specific heat tends to shift to the relatively lower thermodynamic temperature regions as the strength of the crystal field is increased.
A magnetic property of the one dimensional spin 5/2 Ising model under the magnetic field has been investigated by means of transfer matrix method. Thermodynamic response functions are also obtained for varying values of scaling temperature and scaling magnetic field. Entropy and heat capacity of the system were calculated by benefiting from the temperature dependencies of Helmholtz free energy. Our simulation results demonstrate that as the strength of the magnetic field is increased, heat capacity tend to shift to the relatively higher temperature regions, and these findings are consistent with previous results for the low spin values in one dimensional Ising systems.
The ferromagnetic spin-2 quantum Blume-Capel model in the presence of a transverse crystal field interaction is studied by employing a variational approach based on Bogoliubov inequality for the free energy and an exact mapping of the ground state. The thermodynamic properties have been obtained using a single spin cluster, which is equivalent to the usual mean-field approximation. The temperature dependence of the magnetization has been analyzed and the global phase diagram, as function of the model parameters, has been obtained for any values of the coordination number of the lattice. A variety of quantum phase transitions, multiple and multicritical points, are present in several topologies of the corresponding phase diagrams. The ground state properties of the system have also been obtained through an exact mapping of the spin-2 model onto another equivalent spin-1 Blume-Capel model in a transverse field. This mapping allows one to determine an exact asymptote formula of the phase diagram at zero temperature in the limit of large longitudinal crystal field for any lattice dimension.
The thermodynamic properties of a spin S=1/2S=1/2S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating interactions AF1-AF2-AF1-F{\text{AF}}_{1}{\text{-AF}}_{2}{\text{-AF}}_{1}\text{-F}AF1​-AF2​-AF1​-F (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying JAF1=JAF2=JF{J}_{{\text{AF}}_{1}}={J}_{{\text{AF}}_{2}}={J}_{\text{F}}JAF1​​=JAF2​​=JF​ is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the S=1S=1S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.
The thermodynamic properties of the spin S=3/2 ferromagnetic Ising model in the presence of transverse and longitudinal crystal fields (equivalent to the Blume-Capel model with a transverse crystal field) have been studied by using two different approaches: (i) a zero-temperature mapping of the system onto a spin-1/2 quantum Ising model in longitudinal and transverse fields, together with time-independent quantum perturbation theory; and (ii) a standard mean-field approximation within the framework of the Bogoliubov inequality for the free energy. A very rich phase diagram, with different kinds of multicritical behavior, has been obtained. The results show first- and second-order transition lines, tricritical and tetracritical points, critical end points with a two-phase coexistence, double critical end points, and also double noncritical end points. Additionally, the behavior of the magnetization as a function of temperature, over a wide range of values of both longitudinal and transverse crystal fields, has also been analyzed in detail. While large magnitudes of the longitudinal crystal field select the z-spin components either in their states ±3/2 or ±1/2, it is surprising that a large transverse crystal field induces the spin component in the z direction to values ±1, which are completely different from any expected natural component. This comes indeed as a result of the zero-temperature mapping of the ground state with the superposition of the states 3/2 and -1/2, in one sector of the Hilbert space, and the states -3/2 and 1/2 on the other disjoint sector of the Hilbert space. This superposition for a large transverse crystal field prevails even for finite temperatures, implying that the exact critical points are obtained for the model on the one-dimensional lattice and the two-dimensional square lattice, and quite accurate estimates can be achieved for the three-dimensional simple cubic lattice.
The magnetic and thermodynamic properties of spin-1∕21∕21∕2 Heisenberg diamond chains are investigated in three different cases: (a) J1{J}_{1}J1​, J2{J}_{2}J2​, J3>0{J}_{3}>0J3​>0 (frustrated), (b) J1{J}_{1}J1​, J3<0{J}_{3}<0J3​<0, J2>0{J}_{2}>0J2​>0 (frustrated), and (c) J1{J}_{1}J1​, J2>0{J}_{2}>0J2​>0, J3<0{J}_{3}<0J3​<0 (nonfrustrated), where the bond coupling Ji{J}_{i}Ji​ (i=1,2,3)>0(i=1,2,3)>0(i=1,2,3)>0 stands for an antiferromagnetic (AF) interaction, and <0<0<0 for a ferromagnetic (F) interaction. The density-matrix renormalization-group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer-matrix renormalization-group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin-correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor S(q)S(q)S(q) shows peaks at wave vectors $q=a\ensuremath{\pi}∕3$ (a=0,1,2,3,4,5)(a=0,1,2,3,4,5)(a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however, in the magnetic fields where the magnetization plateau with m=1∕6m=1∕6m=1∕6 pertains, exhibits the peaks only at q=0q=0q=0, $2\ensuremath{\pi}∕3$, and $4\ensuremath{\pi}∕3$, which are found to be couplings independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the magnetization, susceptibility, and specific heat show various behaviors for different couplings. The double-peak structures of the susceptibility, and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the XXZXXZXXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat, and magnetization for the compound Cu3(CO3)2(OH)2{\mathrm{Cu}}_{3}{(\mathrm{C}{\mathrm{O}}_{3})}_{2}{(\mathrm{O}\mathrm{H})}_{2}Cu3​(CO3​)2​(OH)2​ are fairly compared with our TMRG results.
In the present paper, the specific heat and magnetic property studies of a spin-1/2 Ising-Heisenberg Cairo pentagonal structure are reported. The model has been comprehensively investigated by F. C. Rodrigues {\it et al.} in Ref. \cite{Rodrigues} without external magnetic field. Here, we consider the mentioned Cairo pentagonal model in the presence of an external tunable magnetic field and examine the low-temperature magnetization process, as well as, the specific heat of the model by using the transfer matrix approach. We find that the model shows magnetization intermediate plateaus at zero and 12\frac{1}{2}21​ of the saturation magnetization accompanied with the growing single Schottky peak in the specific heat curve versus temperature. Each magnetization jump is in accordance with the merging of each two peaks of the specific heat curve when the magnetic field increases. This is reminiscent of the ground state phase transition from one plateau to one another. We also deduce that the magnetic field and the isotropic coupling constant considered for the dimers have substantial effects on the temperature dependence of the specific heat.