Surface modes with biquadratic coupling and uniaxial anisotropy in semi-infinite Heisenberg antiferromagnet

We address the role and the influence of both biquadratic exchange and uniaxial anisotropy in the study of bulk and surface magnetic excitations for a two-sublattices semi-infinite Heisenberg antiferromagnet. The calculations apply to combined effect and are based on a matching technique within the framework of both non-interacting spin-wave theory and random phase approximation. Emphasis has been laid upon the advantage of handling bulk and surface spin precessional fields, characterized by their symmetry in particular. Analytic expressions for the bulk and surface equations of motion are also derived which enables us to analyze qualitatively the nature of the modes by observing the response of the energy branches to the variation of both biquadratic exchange and single-ion anisotropy field as well as exchange parameters occurring on the surface. Two numerical applications of the theoretical formalism developed in this work are described. First concerns the situation when the free surface model is assumed. The second application considers the existence of surface perturbations and treats the effects of the presence of biquadratic exchange term on the bulk and surface spin-wave spectra showing two kinds of surface propagating modes which depend on the presence or not of the uniaxial anisotropy contribution and also on the variations of the bulk-surface exchange parameters. A significant conclusion which this work reached relates to the checking of the results obtained in the literature by using our own theoretical formalism. We show that this formalism is very well adapted to calculations of localized bulk and surface spin-wave modes associated with the simultaneous presence of biquadratic exchange and uniaxial anisotropy. Also, the results obtained for the bulk spin fluctuations field as well as for the magnetic surface waves, are found to be in qualitative agreement with those obtained in the literature. The analytic formulation presented in this work provides an accurate and practical scheme for calculating the surface spin dynamics under the influence of surface exchange parameters, biquadratic coupling and uniaxial anisotropy terms.     

Heisenberg-Dirac-van Vleck vector model for a 1D antiferromagnetic chain of localized spins <Emphasis Type="Italic">S</Emphasis> = 1

Magnetic properties of anisotropic crystals with localized spins S = 1 are investigated; for these crystals, the Hamiltonian is derived in the Heisenberg-Dirac-van Vleck form, which includes biquadratic contributions apart from bilinear terms. The ground-state energy of the antiferromagnetic chain of spins S = 1 is calculated in the model of nearest neighbors, and the interaction constant is renormalized using the renorm group method in the case of coarsening of the system. The temperature criterion for the formation of long-range order in the system is obtained. The excitations of this chain in the linear approximation have a dispersion relation differing from that for antiferromagnets with spin S = 1/2 and are separated by an energy gap from the ground state. Allowance for nonlinear contribution leads to the formation of a solitary wave in the form of a dark-bright soliton.     

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.     

Origin of biquadratic exchange in Fe/Si/Fe

The thickness and temperature dependences of the interlayer exchange coupling in well-defined molecular beam epitaxy-grown Fe/Si/Fe sandwich structures have been studied. The biquadratic coupling shows a strong temperature dependence in contrast to the bilinear coupling. Both depend exponentially on thickness. These observations can be well understood in the framework of Slonczewski's loose spins model [J. Appl. Phys. 73, 5957 (1993)]. No bilinear contribution of the loose spins to the coupling was observed.     

梳型高分子聚合物向列相液晶的相变

本文根据Freiser关于向列相液晶分子相互作用模型,利用平均场理论,建立了梳型高分子聚合物向列相液晶分子的哈密顿量,导出序参数自洽方程,得到各向同性相至单轴向列相以及单轴至双轴向列相的相变,结果表明,当分子主、侧链耦合项中排斥作用及主、侧链中较强向列相场的场强增大时,单轴至双轴向列相相变温度升高,并从一级相变逐渐变为二级相变。 关键词：     

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.     

Equilibrium properties of a spin-1 Ising system with bilinear,biquadratic and odd interactions

The equilibrium properties of the spin-1 Ising system Hamiltonian with arbitrary bilinear (J), biquadratic (K) and odd (L), which is also called dipolar-quadrupolar, interactions is studied for zero magnetic field in the lowest approximation of the cluster variation method. The odd interaction is combined with the bilinear (dipolar) and biquadratic (quadrupolar) exchange interactions by the geometric mean. In this system, phase transitions depend on the ratio of the coupling parameters, α = J/K; therefore, the dependence of the nature of the phase transition on α is investigated extensively and it is found that for α ⩽ 1 and α ⩾ 2000 a second-order phase transition occurs, and for 1 < α < 2000 a first-order phase transition occurs. The critical temperatures in the case of a second-order phase transition and the upper and lower limits of stability temperature in the case of a first-order phase transition are obtained for different values of α calculated using the Hessian determinant. The first-order phase transition temperatures are found by using the free energy values while increasing and decreasing the temperature. Besides the stable branches of the order parameters, we establish also the metastable and unstable parts of these curves and the thermal variations of these solutions as a function of the reduced temperature are investigated. The unstable solutions for the first-order phase transitions are obtained by displaying the free energy surfaces in the form of a contour map. Results are compared with the spin-1 Ising system Hamiltonian with the bilinear and biquadratic interactions and it is found that the odd interaction greatly influences the phase transitions.     

Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling

The mixed spin-1 and spin-3/2 Blume-Emery-Griffiths model with attractive biquadratic coupling is investigated in the framework of the Migdal-Kadanoff Renormalization Group method. By changing the ratio R > 0 of biquadratic and bilinear exchange interactions and according to the different values of crystal field interactions, we have determined six main types of phase diagrams. The full flow in the parameters space of the Hamiltonian was established and the fixed points obtained are drawn up in a table. In addition, we have determined the eigenvalues of the transformation of the group in the vicinity of the critical points. Finally, the introduction of a positive biquadratic interaction was discussed.

     

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.     

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.     

The Curie temperature of a spin-one Heisenberg ferromagnet with biquadratic exchange and uniaxial anisotropy

With the pair model approximation, the Curie temperature of a spin-one Heisenberg ferromagnet with biquadratic exchange interaction J' and uniaxial anisotropy term D is calculated for both positive as well as negative values of J' and D.     

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.     

Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF(2)(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (T(N) = 78.4 K). This is a surprising result given that the AF's uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF(2) crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below T(N), the exchange bias field H(E) measured via FMR for the Ni sample was in good agreement with H(E) determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < T(N), indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM-AF coupling is important at temperatures below and above T(N).     

Spin-flop coupling and exchange anisotropy in ferromagnetic/antiferromagnetic bilayers

By investigating the antiferromagnetic spin configuration, the exchange anisotropy and the interfacial spin-flop coupling in ferromagnetic/antiferromagnetic (FM/AF) bilayers have been discussed in detail. The results show that there are four possible cases for the AF spins, namely the reversible recovering case, irreversible half-rotating case, irreversible reversing and irreversible half-reversing cases. Moreover, the realization of the cases strongly depends on interface quadratic coupling, interface spin-flop (biquadratic) coupling and AF thickness. The magnetic phase diagram in terms of the AF thickness t_AF, the interfacial bilinear coupling J₁ and the spin-flop coupling J₂ has been constructed. The corresponding critical parameters in which the exchange bias will occur or approach saturation have been also presented. Specially, the small spin-flop exchange coupling may result in an exchange bias without the interfacial bilinear exchange coupling. However, in general, the spin-flop exchange coupling can weaken or eliminate the exchange bias, but always enhances the coercivity greatly.     

Low-temperature properties of ferromagnetic Fibonacci superlattices

Theoretical analysis of the layered quasi-periodic Fibonacci structures (superlattices-sequence) is presented for the systems consisting of n_A and n_B ferromagnetically ordered planes within the layers with S_a and S_b spins, respectively, while the interfaces are coupled with bilinear and/or biquadratic exchange interaction, within the framework of localized spin model in the low-temperature limit. Transfer matrix method and direct diagonalization after the bosonization in Bloch's approximation resulted both in the same analytical expression for the magnon-excitation energy. The equivalence (at low-temperatures) of the transfer matrix (spin) and boson approach was discussed, as well as the role of the interlayer biquadratic coupling between different blocks constituting the Fibonacci sequences. Also, our approach allows the determination of the internal energy and calculation of the magnon contribution to the specific heat. It was clearly demonstrated that the magnon specific heat vanishes for T → 0. Our results are compared with the results of other authors.     

Origin of magnetic anisotropy of Gd metal

Using first-principles theory, we have calculated the energy of Gd as a function of spin direction, theta, between the c and a axes and found good agreement with experiment for both the total magnetic anisotropy energy and its angular dependence. The calculated low temperature direction of the magnetic moment lies at an angle of 20 degrees to the c axis. The calculated magnetic anisotropy energy of Gd metal is due to a unique mechanism involving a contribution of 7.5 microeV from the classical dipole-dipole interaction between spins plus a contribution of 16 microeV due to the spin-orbit interaction of the conduction electrons. The 4f spin polarizes the conduction electrons via exchange interaction, which transfers the magnetic anisotropy of the conduction electrons to the 4f spin.     

Heisenberg-type ferromagnetic films with a sandwich structure

Green’s function theory is applied to an alternating two-element multilayer ferromagnetic film. The Hamiltonian is based on the Heisenberg model with a second-order uniaxial single-ion anisotropy and with the interaction between the layer in the interfaces. Magnetization and the phase transition in such system are derived for several sets of material parameters.     

Entanglement detection in the mixed-spin Ising–XY model

In the present work, we initially verify anisotropy effect on the heat capacity of a mixed-three-spin(1/2,1,1/2) system(where spins(1/2,1/2) have XY interaction and spins(1,1/2) have Ising interaction together) at finite temperatures, then,the pairwise entanglement for spins(1/2,1/2), by means of negativity(as a measure of entanglement) as a function of the temperature T, homogeneous magnetic field B, and anisotropy parameter γ is investigated. In addition, we show that one can find magnetic phase transition points for the spins(1/2,1/2) at finite temperatures and understand properly their behavior with respect to the magnetic field and the anisotropy parameter, via the negativity function. An interval of the magnetic field from the negativity diagram of the spins(1/2,1/2) is presented in which quantum phase transition occurs for the tripartite mixed-three-spin system. Finally, some new interesting entanglement witnesses are introduced by using non-degenerate perturbation theory for the mixed-three-spin system.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.