Magnetic properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Rachidi Yessoufou ◽  
Saliou Amoussa ◽  
Felix Hontinfinde
Keyword(s):  
Magnetic Properties ◽  
Phase Transitions ◽  
Crystal Field ◽  
Cayley Tree ◽  
Second Order ◽  
Coordination Numbers ◽  
First Order ◽  
Mixed Spin ◽  
Second Order Transition ◽  
Zero Values

AbstractWe use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ1 and Δ2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D A = Δ1/J,D B = Δ2/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D A or D B increases. The first-order transitions only exist for some appropriate non-zero values of D A and/or D B. The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β 0 of the model is estimated and found to be ¼ at small values of D A = D B = D and β 0 = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.

Critical behaviors and phase diagrams of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising model on the Bethe lattice (BL)

2015 ◽  
Vol 29 (28) ◽  
pp. 1550194 ◽  
Author(s):  
M. Karimou ◽  
R. Yessoufou ◽  
F. Hontinfinde
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Ground State ◽  
Tricritical Point ◽  
Bethe Lattice ◽  
Second Order ◽  
Temperature Phase ◽  
First Order ◽  
Crystal Fields ◽  
Mixed Spin

Using the recursion equations technique, the influences of the single-ion anisotropies or crystal-fields interactions on the magnetic properties of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising ferrimagnetic system are studied on the Bethe lattice (BL). The ground-state phase diagram is constructed, the thermal behaviors of the order-parameters and the free-energy are thoroughly investigated in order to characterize the nature of the phase transitions and to obtain the phase transition temperature. Then, the temperature phase diagrams are obtained in the case of equal crystal-field interactions on the ([Formula: see text] and [Formula: see text]) planes when q = 3, 4 and 6 and in the case of unequal crystal-fields interactions on the ([Formula: see text] and [Formula: see text]) and [Formula: see text] and [Formula: see text]) planes for selected values of [Formula: see text] and [Formula: see text] respectively when q = 3. The model shows first-order and second-order phase transitions, and where the lines are connected is the tricritical point. Besides the first-order and second-order phase transitions, the system also exhibits compensation temperatures depending on appropriate values of the crystal-fields interactions.

The mixed spin-1/2 and spin-1 model with alternating coordination number

2019 ◽  
Vol 33 (11) ◽  
pp. 1950102
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Coordination Number ◽  
Bethe Lattice ◽  
Recursion Relations ◽  
Coordination Numbers ◽  
First Order ◽  
Mixed Spin ◽  
Phase Transition Temperatures ◽  
First Order Phase

The mixed spin-1/2 and spin-1 Blume–Capel model is studied with randomly alternated coordination numbers (CN) on the Bethe lattice (BL) by utilizing the exact recursion relations. Two different CNs are randomly distributed on the BL by using the standard–random (SR) approach. It is observed that this model presents first-order phase transitions and tricritical points for variations of CNs 3 and 4, even if these behaviors are not displayed for the regular mixed-spin on the BL. The phase diagrams are mapped by obtaining the phase transition temperatures of the first- and second-order on several planes.

NMR · NQR and DTA · DSC Studies of Phase Transitions in Pyridinium Tetrachloropalladate(II) and Pyridinium Tetrachloroplatinate(II)

1998 ◽  
Vol 53 (6-7) ◽  
pp. 419-426 ◽  
Author(s):  
Tetsuo Asaji ◽  
Keizo Horiuchi ◽  
Takehiko Chiba ◽  
Takashige Shimizu ◽  
Ryuichi Ikeda
Keyword(s):  
Phase Transitions ◽  
Low Temperatures ◽  
Structural Phase ◽  
Orientational Order ◽  
Second Order ◽  
Order Transition ◽  
Spin Lattice Relaxation ◽  
Potential Wells ◽  
H Nmr ◽  
Second Order Transition

Abstract From the measurements of DTA • DSC and the temperature dependences of 35Cl NQR frequencies, phase transitions were detected at 150 K, 168 K, and 172 K for (pyH)2 [PtCl4], and at 241 K for (PyH)2 [PdCl4]. In order to elucidate the motional state of the constituent ions in the crystals in connection with the structural phase transitions, the 35Cl NQR and 1H NMR spin-lattice relaxation times and the second moment of the 1H NMR line were measured as functions of temperature. For both compounds, the potential wells for the cationic reorientation are suggested to be highly nonequivalent at low temperatures. Above 168 K, the pyridinium ions in (pyH)2[PtCl4] are expected to reorient between almost equivalent potential wells. As for (pyH)2[PdCl4], it is expected that the orientational order of the cation still remains even above the second order transition at 241 K. A change of the potential curve from two-unequal to three-unequal wells is proposed as a possible mechanism of the second order transition. The activation energies for the cationic motion in the respective model potential are derived for both compounds at high and low temperatures.

scholarly journals Ab Initio Non-Covalent Crystal Field Theory for Lanthanide Complexes: A Multiconfigurational Non-Orthogonal Group Functions Approach

2020 ◽  
Author(s):  
Alessandro Soncini ◽  
MATTEO PICCARDO
Keyword(s):  
Magnetic Properties ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Crystal Field ◽  
Orthogonal Group ◽  
Lanthanide Complexes ◽  
Field Energy ◽  
First Order ◽  
Group Functions ◽  
Metal Ligand

We present a non-orthogonal fragment ab initio methodology for the calculation of crystal field energy levels and magnetic properties in lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach has two steps. In the first step, appropriate ab initio wavefunctions for the various ionic fragments (lanthanide ion and coordinating ligands) are separately optimized, accounting for the electrostatic influence of the surrounding environment, within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGF), and reduced to an effective (2J+1)-dimensional non-orthogonal Configuration Interaction (CI) problem via L{\"o}wdin-partitioning. Within the proposed formalism, the projected Hamiltonian can be implemented to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions are systematic approximations to the crystal field energies and wavefunctions. We present a preliminary implementation of the proposed MC-NOGF method to first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach Fragment Ab Initio Model Potential (FAIMP) approximation, and with the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We find that energies and magnetic properties for 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method, compare remarkably well to the full CAHF/CASCI-SO method including metal-ligand covalency, and are superior to the best purely electrostatic results achieved via an iteratively optimized version of the FAIMP approach.<br>

Mixed spin-3/2 and spin-2 nanowire: magnetic properties and hysteresis behaviors

2021 ◽  
Vol 17 (3) ◽  
pp. 615-629
Author(s):  
Karima El Kihel ◽  
Rachid Aharrouch ◽  
Yahya Al Qahoom ◽  
Mohamed Madani ◽  
Nabil Hachem ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Exchange Interaction ◽  
Crystal Field ◽  
Hysteresis Loops ◽  
Magnetic Nanowires ◽  
Content Type ◽  
Mixed Spins ◽  
Mixed Spin ◽  
Compensation Behavior ◽  
Hamiltonian Parameters

PurposeThe purpose of this article is to investigate the magnetic properties and the hysteresis loops behavior of a ferrimagnetic cubic nanowire with mixed spins SA = 3/2 and SB = 2.Design/methodology/approachWe have used the Monte Carlo simulation to examine the influences of the exchange interaction JB, the crystal field ∆ and the temperature on the magnetic properties and hysteresis loops of the nanowire. More exactly, we have shown the temperature dependence of the sublattice magnetizations (mA and mB) and the total magnetization (M) for several values of the Hamiltonian parameters, as well as the corresponding phase diagrams. Finally, the effect of an external magnetic field is studied by plotting the hysteresis loops of the system for different values of exchange interaction, crystal field and temperature.FindingsThe obtained results show the existence of second-order phase transitions, as well as the compensation behavior. Moreover, according to the values of the Hamiltonian parameters, the system can exhibit one, two or three hysteresis loops.Originality/valueThe magnetic nanowires are of great interest in experimental works, but without theoretical explanations, the experimental results cannot be clarified in depth. For this, we contribute through this theoretical study to understand the nanowires, especially those with mixed spins (2, 3/2).

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