Green function theory of anisotropic Heisenberg Ferromagnet with biquadratic exchange

The effects of biquadratic exchange interaction and the uniaxial anisotropy on the curie temperature of the Heisenberg Ferromagnet with spin-one has been studied. Green function technique with random phase approximation has been used. The variation of curie temperature with biquadratic and anisotropic parameters for different lattices has been discussed.     

Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

The phase states of the 2D non-Heisenberg ferromagnetic with anisotropic bilinear and biquadratic exchange interactions are investigated. The limiting cases of the system under consideration are the two-dimensional XY-model with biquadratic exchange interaction and the isotropic Heisenberg ferromagnetic. The account of the magnetic dipole interaction leads to the realization of spatially inhomogeneous quadrupolar phase. The stability regions of various phase transitions for different values of the material parameters are studied. The phase diagram is built. Besides, the temperature phase transitions are investigated. The influence of the magnetoelastic interaction on the formation of the long-range quadrupolar order is determined.     

Critical temperature of an anisotropic ferromagnet in the presence of biquadratic exchange

A formulation, using the double time Green's function method, is presented for the anisotropic spin-one ferromagnetic system in the presence of biquadratic exchange and an expression is given for the critical temperature T_c in terms of parameters associated with the uniaxial anisotropy (treated exactly) and the biquadratic interaction (only the longitudinal part, treated in RPA). The prediction that T_c increases with the biquadratic exchange is found to be consistent with the recent calculation.     

Spin 1 frustrated antiferromagnet with biquadratic exchange and single ion anisotropy

The zero temperature properties, using the bond operator technique, are determined for the frustrated S=1 Heisenberg antiferromagnetic model plus nearest-neighbor biquadratic exchange interaction and single ion anisotropy on a two dimensional square lattice.     

Quantum Breathers in an Anisotropic Ferromagnetic Heisenberg Chain with Biquadratic Exchange Interaction

Based on the Hartree approximation and the semidiscrete multiple-scale method, quantum breathers in an anisotropic ferromagnetic Heisenberg chain with biquadratic exchange interaction are predicted analytically. The existence condition of quantum breathers is obtained, and the properties of quantum breathers are analyzed. Moreover, it is shown that the energy of such quantum breathers is quantized.     

Anisotropic ferromagnet with biquadratic exchange

A formulation, using the double time Green’s function method, is presented for the anisotropic spin-one ferromagnetic system in the presence of Ising part of the biquadratic exchange and an expression is given for the critical temperatureT _c in terms of two parameters. One is associated with the uniaxial anisotropy (treated exactly) and the other one corresponds to the biquadratic interaction (treated in RPA). The bilinear Heisenberg exchange term is treated in Callen’s approximation emphasizing the role of intersite correlation for small parameters. The prediction thatT _c increases with the biquadratic exchange is found to be consistent with the recent calculation based on high temperature series expansion.     

Magnetization curves of a spin-one Bethe lattice

An exact calculation of the spontaneous magnetization of a spin-one Ising model with the inclusion of biquadratic exchange and single ion anisotropy on the Bethe lattice is presented. The magnetization curves exhibit some unusual features as the relative strength of the single ion anisotropy is varied.     

具有四次幂交换作用的Heisenberg铁磁体的低温自旋波理论

本文讨论具有四次幂交换作用的Heisenberg铁磁体,用Малеев玻色变换,在低温区建立〈S_i^z〉的严格展式,正确地包括了动力学相互作用和运动学相互作用,得到自旋波谱和自发磁化的正确温度依赖关系。 关键词：     

Re-entrant phase transitions of the Blume-Emery-Griffiths model

We have investigated the spin-1 Ising model on the simple cubic lattice with bilinear, biquadratic interaction and anisotropic energy (BEG model). We have been specially interested in the case of antiferro biquadratic interaction, because the interaction will cause the competition with bilinear interaction and anisotropy. A two-sublattice ordering, so called the staggered quadrupole (SQ) phase, occurs as long as biquadratic interaction is negative large enough. We have obtained a full phase diagram in the whole interaction parameter space (for the positive bilinear interaction) by the Bethe approximation, and found several kinds of phase transitions, such as successive, re-entrant and double re-entrant transitions. These transitions are also confirmed by Monte Carlo simulations on simple cubic lattices.     

Spiral magnetic structure in Heisenberg and non-Heisenberg magnets

The possibility of forming a modulated (spiral) magnetic structure in anisotropic Heisenberg and non-Heisenberg magnets with a frustrated Heisenberg exchange interaction has been investigated. It has been demonstrated that, apart from homogeneous (ferromagnetic and quadrupole) states, the Heisenberg magnets with a strong easy-plane anisotropy can have a spiral magnetic structure. The axis of the spiral coincides with the direction of the external magnetic field. The inclusion of the biquadratic exchange interaction leads to a narrowing of the magnetic field region of the existence of the spiral structure. In the absence of the external magnetic field, the spiral structure can be formed only in the case of easy-axis anisotropy.     

Many-electron exchange Hamiltonian in the theory of ferromagnetism

A Hamiltonian describing effects of many-electron interatomic exchange in magnetic crystals is derived by application of an appropriate unitary transformation to the many-electron, many-nucleus Hamiltonian. It is expressed in terms of atomic annihilation and creation operators and j-fold exchange matrix elements for 1 ? j ? N, where N is the number of electrons localized on each crystal site. Explicit formulas are derived for the case of not more than half-filled shells with Hund's rule factorization. An appropriate spin algebra is introduced and the coefficient of the bilinear (Heisenberg) and biquadratic interactions evaluated in terms of single and double-exchange matrix elements. The relative magnitudes of such matrix elements are roughly estimated using determinantal wave functions.     

Renormalization group treatment of a spin-one Ising model with biquadratic exchange interaction

The critical behavior of a spin-one Ising model with biquadratic exchange interactions is studied using the mean field renormalization group method. The phase diagram for various lattices is obtained. The nature of the phase transition with biquadratic interaction is analysed and comparison with other methods is made.     

Exchange effect and magneto-plasmon mode dispersion in an anisotropic two-dimensional electronic system

The exchange effect and the magneto-plasmon mode dispersion are studied theoretically for an anisotropic twodimensional electronic system in the presence of a uniform perpendicular magnetic field.Employing an effective lowenergy model with anisotropic effective masses,which is relevant for a monolayer of phosphorus,the exchange effect due to the electron-electron interaction is treated within the self-consistent Hartree-Fock approximation.The magnetoplasmon mode dispersion is obtained by solving a Bethe-Salpeter equation for the electron density-density correlation function within the ladder diagram approximation.It is found that the exchange effect is reduced in the anisotropic system in comparison with the isotropic one.The magneto-plasmon mode dispersion shows a clear dependence on the direction of the wave vector.     

Green function theory of biquadratic heisenberg ferromagnet

The Heisenberg ferromagnet with the biquadratic exchange interaction is studied. The low temperature expansion of magnetization, the Curie temperature and the susceptibility at high temperatures are obtained.     

Reentrant behaviour in Ising models with biquadratic exchange interaction

The critical behaviour for the spin-1 Ising model with biquadratic interaction is investigated in two and three dimensions using the Monte Carlo method. The phase diagram for the three-dimensional system exhibits a reentrant behaviour for large positive values of the biquadratic exchange coupling. The temperature dependence of magnetization and susceptibility in the reentrant region is also presented.     

Exact solution of the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions

We demonstrate explicitly that the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions can be solved exactly. Results are provided for the free energy, equal-time spin-spin correlation functions and the initial susceptibility of the corresponding bond and site model in the annealed and quenched limit. A numerical analysis of the thermodynamic response functions in the n = 3 case is performed, and therein some interesting consequences of the simultaneous influence of the biquadratic interactions and impurities are established. The presence of the biquadratic interaction is interpreted as an effect of the lattice compressibility.     

Intrinsic biquadratic exchange and sublattice magnetizations in canted ferrimagnets

We investigate in a molecular field approximation the influence of an intrinsic biquadratic exchange term on the sublattice magnetizations of a canted ferrimagnet. A comparison is given with an approximate treatment only valid when the origin of the biquadratic term is in magnetostrictive phenomena. The approximate treatment is found to give the correct sign, but to overestimate the effects of the biquadratic term.     

Surface-induced ordering in thin uniaxial liquid crystal films

The interface localization transition in thin uniaxial liquid crystal films with competing surface fields has been studied using Metropolis Monte Carlo simulations. The model is constructed from a lattice of continuously orientable interacting spins, and the Hamiltonian contains both bilinear and biquadratic contributions. The biquadratic contribution to the Hamiltonian is familiar from the Lebwohl-Lasher model, and accounts for the particle anisotropy in a liquid crystal. The head-tail asymmetry of the molecules in a uniaxial liquid crystal is taken into account through a bilinear contribution familiar from the classical ferromagnetic Heisenberg model with exchange anisotropy Lambda. The critical temperature T(c), characterizing the interface localization transition within the uniaxial liquid crystal film, depends strongly on the relative magnitudes of the bilinear and biquadratic interactions between the spins. For systems dominated by the biquadratic interaction, T(c) is found to be close to the bulk critical temperature of the system. But as the biquadratic interaction strength is reduced, T(c) departs markedly from the bulk critical temperature of the system.     

Phase transitions as a function of material constants and temperature in intermetallic compounds of the terfenol-D type

A model of magnetic and magnetoelastic properties of intermetallic compounds has been considered with the inclusion of the influence of the “giant” magnetoelastic coupling and the biquadratic exchange interaction. The phase transitions as a function of material constants and temperature have been investigated in the framework of the proposed model. It has been demonstrated that the ferromagnetic and quadrupole phases can be formed in the system under consideration. In this case, the phase transition between these phases is a first-order transition and occurs through the intermediate, i.e., quadrupole-ferromagnetic, state. The dependences of the phase transition temperature on the Heisenberg and biquadratic exchange interaction constants have been obtained for compounds of the terfenol-D type.