掺杂各向异性三角晶格系统的自旋动力学

在t_J模型和fermion_spin理论框架下，研究了欠掺杂区 各向异性三角晶格反铁磁体的自旋动力学.与掺杂的四方晶格反铁磁体一样，随着掺杂的增大出现了公度到非公度的转变，而且散射峰的位置与各向异性度有关.尽管非公度峰的位置不随能量变化，但其权重随能量的增大而降低.  关键词： t_J模型 fermion_spin理论 三角晶格     

Magnetic transitions in layered triangular antiferromagnets

Magnetic states and phase transitions of the layered triangular antiferromagnets in an applied field are studied. It is shown that in compounds like VBr₂ and VCl₂ quantum effects change the ground-state structure and cause successive phase transitions as the magnetic field increases. Coplanar structures of different spin configuration are realized far from the saturation field and a noncoplanar structure of umbrella-type configuration is realized near this field. The ground-state phase diagram is constructed, and a finite region of fields where the collinear phase is also possible is indicated.     

Yang-Lee zeros of triangular Ising antiferromagnets

In our previous research, by combining both the exact enumeration method (microcanonical transfer matrix) for a small system (L=9) with the Wang-Landau Monte Carlo algorithm for large systems (to L=30) we obtained the exact and approximate densities of states g(M,E), as a function of the magnetization M and exchange energy E, for a triangular-lattice Ising model. In this paper, based on the density of states g(M,E), the precise distribution of the Yang-Lee zeros of triangular-lattice Ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature for a 9×9 lattice system. Also, the feasibility of the Yang-Lee zero approach combined with the Wang-Landau algorithm is demonstrated; as a result, we obtained the magnetic exponents for triangular Ising antiferromagnets at various temperatures.     

On the line-width in critical anisotropic antiferromagnets

We present a calculation of the longitudinal scaling function for the line-width of critical uniaxial antiferromagnets. The agreement with experimental results for MnF₂ is satisfactory.     

The magnetic order of two-dimensional anisotropic antiferromagnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature T_N, energy gap w₀ and staggered magnetization m are calculated. The theoretical predictions of T_N and w₀ for K₂NiF₄, Rb₂MnF₄, K₂MnF₄, Rb₂MnCl₄ and (CH₃NH₃)₂MnCl₄ fit well to the measured values. The power law behavior of is also investigated. The exponents β and ν for K₂NiF₄ are in excellent agreement with the experimental results.     

Critical temperatures of the anisotropic Heisenberg antiferromagnets

The first eight terms of the high temperature series expansions for the mean-square fluctuations of the magnetization variables are derived for the spin $\text{?}\text{1}\text{2}$ anisotropic Heisenberg antiferromagnets. The antiferromagnetic critical temperatures are determined for the s.c. and b.c.c. lattices.     

Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Uniaxially anisotropic antiferromagnets in a field on a square lattice

Classical uniaxially anisotropic Heisenberg and XY antiferromagnets in a field along the easy axis on a square lattice are analysed, applying ground state considerations and Monte Carlo techniques. The models are known to display antiferromagnetic and spin-flop phases. In the Heisenberg case, a single-ion anisotropy is added to the XXZ antiferromagnet, enhancing or competing with the uniaxial exchange anisotropy. Its effect on the stability of non-collinear structures of biconical type is studied. In the case of the anisotropic XY antiferromagnet, the transition region between the antiferromagnetic and spin-flop phases is found to be dominated by degenerate bidirectional fluctuations. The phase diagram is observed to resemble closely that of the XXZ antiferromagnet without single-ion anisotropy.     

Spin-wave analysis of easy-axis quantum antiferromagnets on the triangular lattice

We perform the standard spin wave analysis of the triangular Heisenberg quantum antiferromagnet with nearest neighbour coupling. The exchange interaction is taken to be J _{z=J x=J y} (0<1). We give a simple explanation of the non-trivial classical degeneracy pointed out by Miyashita and Kawamura and show that it is removed by quantum fluctuations, but that the degeneracy manifests itself through the appearance of a second gapless spin-wave branch. The existence of a second gapless mode has a drastic influence on the quasiclassical behaviour near the Ising limit: the energy gain with respect to the Ising state energy is found to be linear in , and the reduction of the sublattice magnetization on two of the three sublattices remains finite as 0. These findings essentially invalidate the original qualitative arguments [14] in favour of a spin-liquid ground state of the anisotropic triangular antiferromagnet.     

Low-lying excited states of quantum antiferromagnets on a triangular lattice

We study low-lying states of theXY and Heisenberg antiferromagnets on a triangular lattice to clarify whether spontaneous symmetry breaking occurs atT=0 in the thermodynamic limit. Approximate forms of low-lying states are proposed, in which degrees of freedom of the sublattice magnetization and of the chirality are separated. These approximate states have a long-range order and twofold structures. It is shown that low-lying states can be accurately described with the present approximation. It has been argued that low-lying states play an important role in symmetry breaking. With the help of this approximation, we discuss the contribution of low-lying states to symmetry breaking of two types, namely creation of the spontaneous sublattice magnetization and the spontaneous chirality. Furthermore, to show evidence for the occurrence of symmetry breaking, we numerically study the low-lying states of finite systems of theXY and Heisenberg antiferromagnets. It is found that the necessary conditions for the symmetry breaking to occur are satisfied in these models.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

The magnetic properties of three-dimensional spin-1 easy-axis single-ion anisotropic antiferromagnets

The ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are studied. By using of the double-time Green’s function method within the Tyablikov decoupling for the exchange anisotropy and Callen’s approximation for the single-ion anisotropy, the Néel temperature, magnetization and susceptibility are investigated. Their relations with the temperature and anisotropic parameter are analyzed over the entire range of temperature. It is found that our results agree well with spin wave theory results at low temperature, agree with the high temperature series results at high temperature, and compare reasonably well with the linked-cluster series approach and ratio method results at intermediate temperature.