Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouring interactions

By using the method of density-matrix renormalization-group to solve the different spin spin correlation functions, the nearest-neighbouring entanglement （NNE） and the next-nearest-neighbouring entanglement （NNNE） of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearestneighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring （NNN） interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.     

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.     

First-principle investigation of the electronic and magnetic properties of PbMn（SO4）2

The magnetic properties of oxide PbMn(SO₄)₂ consisted of MnO₆ octahedra which connected with each other through SO₄ tetrahedra, are well studied in experiments. In this paper, we explored its interesting electronic and magnetic properties with first-principle calculations. Our results show that all Mn ions have high spin states, namely, S = 5/2, and the magnetic couplings between NN and NNN are antiferromagnetic, which agree well with the experimental results. Besides, the surprising results of spin exchange interactions between the NN and NNN are excellently explained with extended Hückel tight-binding calculations.     

Self-Trapping in Discrete Nonlinear Schrdinger Equation with Next-Nearest Neighbor Interaction

The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.     

Magnetic phase diagram of an extended Hubbard model at half filling: Possible application for strongly correlated iron pnictides

We study the magnetic phase diagram within an extended half-filled Hubbard model, focusing on the roles of the next-nearest-neighbor (NNN) and the next-next-nearest-neighbor (3rd NN) hoppings in the magnetic configurations. We find that due to the spin frustration from the long range hopping and the competition between long-range hopping and Coulomb correlation, the striped antiferromagnetic (AFM) phase is stable when the NNN hopping is dominant, while the bicollinear AFM phase is robust when the 3rd NN hopping is considerably large. The triple points are found in various magnetic phase diagrams. Possible applications of the present theory on intermediately correlated LaFeAsO and strongly correlated FeTe are discussed.     

Quantum fluctuations and ground state of weakly interacting helix spin chains in a magnetic field

Ferromagnetic spin chains of a hexagonal lattice coupled by a weak antiferromagnetic interaction J₁ develop a helix arrangement if the intrachain antiferromagnetic NNN exchange J₂ is sufficiently large. We show that the classical minimum energy spin configuration is an umbrella when an external magnetic field is applied. The scenario is dramatically changed by quantum fluctuations. Indeed we find that the zero point motion forces the spins in a plane containing the magnetic field so that classical expectation is deceptive for our model. Our result is obtained by controlled expansion in the low field-long wavelength modulation limit. Received: 9 September 1997 / Revised: 15 October 1997 / Accepted: 17 November 1997     

Integrable correlated electron model with next-nearest-neighbour interactions

The exactly solvable model of supersymmetric t - J chains (STJC) of correlated electrons with next-nearest-neighbour (NNN) interactions is proposed and studied. The model with interactions between nearest neighbours and NNN interactions in one chain can also be considered as a two-chain model with zigzag-like coupling between the chains. The NNN interaction (coupling between chains) causes the onset of additional Dirac seas for low-lying charge and/or spin excitations. These Dirac seas change the low-energy (conformal) behavior of the model. The filling of those seas depends on the values of the NNN coupling (interactions between chains), external magnetic field and applied voltage. We identify the new ground state phases which appear due to the NNN as incommensurate ones. The NNN coupling in the incommensurate phases induces spontaneous magnetization and/or spontaneous filling of the Dirac sea for charge excitations (“spontaneous charge ordering”). The onset of this order implies a first order quantum phase transition driven by the field with hysteresis phenomena. Received 13 September 2000     

Dynamical and static spin conductivities in the Heisenberg model on honeycomb lattice: The effects of magnetic long range ordering

We have studied both dynamical and static spin conductivities of Heisenberg antiferromagnet on honeycomb lattice in the presence of a magnetic long range ordering. The effects of spatial anisotropy as weak Dzyaloshinskii–Moriya interaction and next nearest neighbor exchange coupling on the behaviors of conductivities are discussed. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. Using Holstein–Primakoff bosonic transformations, the behaviors of spin transport properties have been studied by means of excitation spectrum of mapped bosonic gas. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various Dzyaloshinskii–Moriya interaction strengths. Furthermore we have studied the frequency dependence of dynamical spin conductivity for various Dzyaloshinskii–Moriya interaction strengths and different next nearest neighbor coupling constants. We find that the height of peak in the temperature dependence of static spin conductivity increases upon increasing the anisotropy parameter. The static spin conductivity is found to be monotonically increasing with anisotropy parameter due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different next nearest neighbor coupling constants.     

Co-Ni/FeMn双层膜中磁化强度对交换偏置的影响

固定CoNiFeMn双层膜中反铁磁层的厚度,改变CoNi铁磁层的成分来调节磁化强度,从而研究铁磁层的饱和磁化强度对CoNiFeMn双层膜中交换偏置的影响.研究表明,CoNiFeMn界面的交换耦合能U不是一个常量,而是随(MFM)12的增加而线性增加.其原因是铁磁层磁矩通过界面相互作用在反铁磁层中形成的局域交换磁场,在磁场冷却时影响反铁磁层的自旋结构或磁畴结构及双层膜中的交换偏置 关键词： 交换偏置 磁化强度     

Biaxial magnetic structures in rare-earth compounds: GdMg and HoP

The flopside spin structure, where the magnetic moments form two sublattices which at low temperatures are mutually perpendicular was first found in HoP and then in other rare-earth pnictides. There are large orbital contributions to the magnetic moments of these compounds and it had been thought that they play an important role in stabilizing the flopside spin structure. However, recently this spin structure has been found in GdMg. As Gd³⁺ is an S-state ion, there are negligible orbital effects. We have developed a model Hamiltonian which is able to explain both the occurence of initially a ferromagnetic phase and then at low temperature the flopside spin structure in two very dissimilar compounds GdMg and HoP. For GdMg we find that the competition between the near neighbor ferromagnetic and antiferromagnetic bilinear exchange interactions is such that while they produce a transition to a ferromagnetic phase at 110 K, an unusually small amount of biquadratic (quadrupolar) coupling is able to stabilize a flopside phase at low temperature which is able to resist collapse in a field as large as 150 kOe. For HoP we find that although anisotropic bilinear pair interactions - as for example pseudo-dipole - exist, they cannot be the primary origin of the flopside phase; quadrupole pair interactions are essential to explain the appearance of first the ferromagnetic and then the flopside phases found in HoP. On the basis of our model calculations we are able to explain the data extant on these compounds and we make some predictions which are open to experimental verification.     

Effects of spin-wave energy degeneracy induced by in-plane wave propagation in ferromagnetic thin films

This work presents an investigation of the collapse effect predicted to occur in the spin-wave band structure of magnetic cubic thin films. The system under consideration is described by the Heisenberg model with exchange interactions between the nearest (NN) and next-nearest neighbors (NNN) taken into account. In the collapse effect, which occurs for some specific directions of in-plane propagation of spin waves, the effective coupling between spins in adjacent layers vanishes dynamically and each mode becomes confined to a single atomic plane; this means that all the bulk modes and, independently, all the surface modes become energetically degenerate. This effect of ‘directional collapse’ can only occur when the exchange interactions between NN or NNN include bonds oblique with respect to the direction of in-plane propagation.     

External magnetic field effects on a distorted kagome antiferromagnet

We report bulk magnetization, and elastic and inelastic neutron scattering measurements under an external magnetic field H on the weakly coupled distorted kagome system, Cu2(OD)3Cl. Our results show that the ordered state below 6.7 K is a canted antiferromagnet and consists of large antiferromagnetic ac components and smaller ferromagnetic b components. By first-principles calculations and linear spin wave analysis, we present a simple spin Hamiltonian with nonuniform nearest neighbor exchange interactions resulting in a system of coupled spin trimers with a single-ion anisotropy that can qualitatively reproduce the spin dynamics of Cu2(OD)3Cl.     

量子顺电EuTiO_3材料基态磁性的第一性原理研究

EuTiO_3是钙钛矿结构的量子顺电体,实验发现其基态具有平面各向异性G类反铁磁结构,本文运用基于密度泛函理论的第一性原理计算研究了EuTiO_3处于量子顺电相和应力作用下处于铁电四方相时可能的自旋取向和自旋交换耦合作用,分析了自旋耦合作用的路径,探讨了应力对磁性交换路径的作用,结果发现:当体系自由时,EuTiO_3具有自旋沿[110]方向平面内单轴各向异性的G类反铁磁结构,该结构下Eu离子4f电子自旋通过处于面心位置的O 2p实现自旋反铁磁性的超交换耦合,而在外加应力诱导的铁电四方结构下,由于自旋交换路径中Eu—O—Eu键角改变,Eu 4f电子自旋实现了[110]方向的铁磁交换耦合。     

Specific Heat of a Two-Layer Magnetic Superlattice

The specific heats of both a two-layer ferromagnetic superlattice and atwo-layer ferrimagnetic one are studied. It is found that the spin quantumnumbers, the interlayer and intralayer exchange couplings, the anisotropy,the applied magnetic field, and the temperature all affect the specificheat of these superlattices. For both the ferromagnetic and ferrimagneticsuperlattices, the specific heat decreases with increasing the spin quantumnumber, the absolute value of interlayer exchange coupling, intralayerexchange coupling, and anisotropy, while it increases with increasingtemperature at low temperatures. When an applied magnetic field is enhanced, the specific heat decreases in the two-layer ferromagnetic superlattice, while it is almost unchanged in the two-layer ferrimagnetic superlattice at low field range at low temperatures.     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Entanglement in the Extended XY Spin Model with Three Spin Interaction and External Field

We investigate the pairwise thermal entanglement of the extended XY model with three spin interactions and external filed on zig-zag lattice. The influences of three spin interactions J ₂ and external field λ on the thermal entanglement of the nearest neighbor (NN) and next nearest neighbor (NNN) spins are considered. It is found that J ₂ and λ suppress both the maximal value and the critical temperature of the NN entanglement C ₁₂. However, when it comes to the NNN entanglement C ₁₃, there exists a critical value of J ₂ above which both the maximal entanglement and the critical temperature can be enhanced by J ₂ for a fixed external field. With J ₂ fixed, the effect of λ on C ₁₃ are different for different values of J ₂. For J ₂<1, λ suppresses both T _C and the maximal values of C ₁₃. For J ₂≥1, λ enhances the maximal values of C ₁₃ while decreases the critical temperature. These results show that one is able to get the entanglement wanted by properly controlling the values of the three spin interactions J ₂ and the external field λ.     

Spin Wave Spectra in a Ferromagnetic/Non-magnetic Superlatt ice with Antiparallel Magnetization

The transfer-matrix method is employed to investigate the spin waves in a ferromagnetic/non-magnetic superlat tice with an antiferromagnetic coupling between interfacial ferromagnetic layers across a non-magnetic spacer layers and the an tiparaUel magnetizations between neighboring ferromagnetic films. The dispersion relation of the spin waves is obtained. The effects of the thickness of the magnetic layers, the antiferromagnetic coupling strength and concentration of magnetic atoms at the interface on the spin wave spectra are discussed in detail.     

外应力场下铁磁/反铁磁双层膜系统中的自旋波

采用自由能极小的方法研究了铁磁/反铁磁双层膜系统在外应力场下的一致进动自旋波性质，即铁磁共振现象. 本模型中铁磁层很薄可看成单畴结构，但具有单轴磁晶各向异性和立方磁晶各向异性；而反铁磁层仅具有单轴磁晶各向异性，但其厚度趋于半无穷. 推导出了该系统的铁磁共振频率和频谱宽度的解析式. 结果表明，外应力场和界面交换耦合或反铁磁磁强度仅在弱磁场下对系统的铁磁共振有影响，且系统的铁磁共振行为按磁场强度可分为两支，其区分弱磁场和强磁场的临界场依赖于外应力场的方向. 另一方面，应力场方向的改变可借助于反铁磁层磁畴变化对铁磁层磁晶各向异性轴有影响. 关键词： 铁磁/反铁磁双层膜 界面耦合强度 铁磁共振 应力场