Longitudinal continuum spin conductivity by Kubo formula in the Heisenberg model with bilinear and biquadratic exchange interactions

2020 ◽  
pp. 167657
Author(s):  
L.S. Lima
Keyword(s):  
Heisenberg Model ◽  
Exchange Interactions ◽  
Kubo Formula ◽  
Biquadratic Exchange

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

scholarly journals Обменные взаимодействия в паре ионов Cr-=SUP=-3+-=/SUP=--Cr-=SUP=-3+-=/SUP=- в диамагнитной матрице ABO-=SUB=-3-=/SUB=- (A=Ga, In, Sc)

2020 ◽  
Vol 62 (3) ◽  
pp. 403
Author(s):  
А.М. Воротынов ◽  
В.В. Руденко ◽  
О.В. Воротынова
Keyword(s):  
Magnetic Resonance ◽  
Ion Pairs ◽  
Exchange Interactions ◽  
Resonance Technique ◽  
Biquadratic Exchange ◽  
Magnetic Resonance Technique

Abstract The exchange interactions in the Cr^3+–Cr^3+ ion pairs in the isostructural ABO_3 (A = Ga, In, Sc) diamagnetic compounds have been examined using the magnetic resonance technique. The values of bilinear and biquadratic exchange interactions have been determined. It is shown that the biquadratic exchange in the Cr^3+–Cr^3+ pair in these compounds is caused by the exchange striction.

Thermodynamic Properties of an In-Phase Flux Antiferromagnetic Spin Coupled Heisenberg Model on a Square Lattice

SPIN ◽  
2018 ◽  
Vol 08 (04) ◽  
pp. 1830001
Author(s):  
E. Mainimo ◽  
N. Ibrahim Famenyi
Keyword(s):  
Energy Spectrum ◽  
Specific Heat ◽  
Thermodynamic Parameters ◽  
Heisenberg Model ◽  
State Energy ◽  
Spontaneous Magnetization ◽  
Exchange Interactions ◽  
Spin Model ◽  
Square Lattice ◽  
Antiferromagnetic Spin

Using the two-dimensional Jordan–Wigner Fermionization procedure, we calculate the energy spectrum of the in-phase flux antiferromagnetically spin-1/2 coupled Heisenberg model in a square lattice, the formalism used introduces the notion of isotropic parameters. The energy spectrum is analyzed for various regimes of the exchange interactions and the isotropic parameters. The thermodynamic parameters of the lattice, notably the ground state energy, the free energy, mean energy, entropy and specific heat are calculated. It is seen that the specific heat undergoes a phase transition at a temperature below the critical temperature due to spontaneous magnetization. Its entropy for homogeneous and completely isotropic regime is compared for two regimes of the exchange interaction and it is observed that the entropy decreases with an increase in the coupling strength. All the thermodynamic parameters calculated for this spin model are seen to be in conformity with the principles and laws of Statistical Thermodynamics.

Effect of Biquadratic Exchange Upon Ferromagnetic Two-Magnon Bound States. II. Anisotropic Exchange

1974 ◽  
Vol 52 (1) ◽  
pp. 33-39 ◽  
Author(s):  
D. A. Pink ◽  
R. Ballard
Keyword(s):  
Bound States ◽  
Exchange Interactions ◽  
Bound State ◽  
Exchange Term ◽  
Zero Temperature ◽  
Biquadratic Exchange ◽  
Anisotropic Exchange ◽  
Bound State Spectrum ◽  
Mode Pair ◽  
Isotropic Exchange

We have investigated the two-magnon bound state spectrum of a ferromagnetically ordered system for which the Hamiltonian contains an anisotropic bilinear exchange term, an anisotropic biquadratic exchange term, and a single-ion anisotropy term. The bound states, labelled by a wave vector q which we have taken to be in the [111] direction, were calculated by using zero-temperature Green functions. The principal results are: (i) the existence of single-ion bound states in the absence of single-ion anisotropy and conversely, their absence in the presence of such anisotropy, in contrast to the case in which the exchange interactions are isotropic; (ii) the appearance of an S mode for values of q, [Formula: see text]; (iii) the ordering of bound states for isotropic exchange interactions wherein the S0 mode lies below the S1-mode, D-mode pair and where the S1 mode lies below (above) the D mode if they lie below (above) the band, no longer holds.

scholarly journals Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice

10.14311/1344 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
N. Ananikian ◽  
L. Ananikyan ◽  
L. Chakhmakhchyan ◽  
A. Kocharian
Keyword(s):  
Magnetic Field ◽  
Heisenberg Model ◽  
Quantum Phase Transitions ◽  
Exchange Interactions ◽  
Effective Field ◽  
Threshold Temperature ◽  
Kagome Lattice ◽  
Thermal Entanglement ◽  
Kagomé Lattice ◽  
Bogoliubov Inequality

The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement.

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