Modeling Spectroscopic Properties of Ni2+ Ions in the Haldane Gap System Y2BaNiO5

Modeling of spin Hamiltonian parameters enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions in crystals. In this paper, based on the crystallographic data and utilizing the point-charge model and superposition model, the crystal field parameters (CFPs) are estimated for Ni²⁺(3d ⁸) ions in the Haldane gap system Y₂BaNiO₅. The CFPs serve as input for the perturbation theory expressions and the crystal field analysis package for microscopic spin Hamiltonian modeling of the zero-field splitting parameters (ZFSPs) D and E. Results of an extensive literature search of the pertinent crystallographic data, experimental ZFSPs, and model parameters are briefly outlined. The modeling aims at verification of the experimental ‘single ion anisotropy’ parameters and explanation of the controversy concerning the maximal rhombic distortion |E/D| ≈1/3 reported for Ni²⁺ ions in Y₂BaNiO₅. The preliminary results call for reanalysis of some magnetic studies of the Haldane gap systems.     

Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.     

混合自旋反铁磁材料Y2BaNiO5的磁学和热力学性质

在格林函数的理论框架下,采用一维自旋为1的各向异性Heisenberg模型来讨论Y2BaNiO5材料的磁学和热力学性质.得到了它的自旋关联函数、低激发谱、基态能(Eg)、比热(C)和静态磁化率(χ)在不同交换各向异性因子下的性质,所得结果与实验和数值模拟结果完全一致.     

Transport in quasi one-dimensional spin-1/2 systems

We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.     

Critical properties of mixed spin-1 and spin-5/2 with equal and unequal crystal fields

The effects of assuming equal or unequal crystal fields (CF) on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice (BL). The equal CF case was considered for the coordination numbers q=3, 4, and 6, while for q=3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q=4 and first-order phase transitions and tricritical point (TCP) for q=6. In the unequal CF case for q=3, the system yields first- and second-order phase transitions, TCP's, and three compensation temperatures. In addition, the TCP's in a very short range are classified as the stable and unstable ones depending on their free energies.     

Application of Kemmer-β formalism to spin-1/2 systems

The nonphysical components of Kemmer-β formalism for spin-1/2 particles have been removed. It is shown that in the presence of an external electromagnetic field the formalism is identical with that of Dirac's second-order equation and thus is solvable in specific cases by the usual methods     

Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 1

Electron paramagnetic resonance (EPR) spectra of S=1/2 systems XL(n) with n equivalent nuclei having spin I=1/2 have been simulated for microwave frequencies in the L-, X-, and W-bands. It has been shown that for n>2 nuclei, the EPR spectra have a more complicated form than anticipated from the usual oversimplified analysis, which predicts n+1 lines with intensity ratios given by the coefficients of the binomial expansion. For the XL(n) system with n=3, the EPR spectra in fact consist of six lines. The exact solution of the spin-hamiltonian for this case has been obtained, which gives four levels in zero magnetic field. For n>2 systems, the degeneracy of the energy levels cannot be completely removed by the Zeeman electronic and nuclear interactions. For n>4, certain spin states cannot occur, consistent with the (generalized) Pauli exclusion principle. Discussion of the underlying theory, invoking exchange degeneracy and the appropriate permutation group theory, is included in some detail. Analogous considerations hold for NMR spectroscopy of non-radicals.     

Numerical study of the mixed spin-1 and spin-5/2 BEG model on the Bethe lattice

The mixed spin-1 and spin- \frac52\frac{5}{2} ferromagnetic Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction (D) is studied on the Bethe lattice by means of exact recursion equations. First, the phase diagram of the system at zero temperature is obtained in the (D/Jq, K/Jq) plane, where q denotes the coordination number of the lattice. Second, the sublattice magnetizations as functions of the temperature, the crystal-field and the biquadratic interaction strengths are thoroughly investigated. For q = 3, the resulting phase diagrams show first and second order phase transitions as well as compensation points where the net magnetization of the whole lattice should vanish in the antiferromagnetic version of the model. One interesting feature of the model concerns the presence of tricritical points. Our calculations show that at non-zero temperature, none of the sublattice can order separately. However, under an external magnetic field, some interesting phase diagrams with partially ordered phases arise.     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Some characteristic behavior of mixed spin-1/2 and spin-1 Ising nano-tube

The magnetization of a cylindrical Ising nano-tube is investigated by the use of the effective field theory with correlations. The effects of the crystal field couplings at the surface shell to the order parameters, susceptibility, internal energy, specific heat and free energy are investigated. Some characteristic phenomena are examined in the thermal variations, depending on crystal field term. Moreover, tricritical and critical points are found on the (D/J,kT/J) plane, where D/J and kT/J are reduced crystal-field and temperature, respectively.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT).In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ++ and Δ + are found to agree well with data within the experimental uncertainties.     

Quantum mechanics of ‘free’ spin-1/2 particles in an expanding universe

This paper deals with the gravi-quantum mechanical interaction on the level of the first quantisation and in the framework of a metric theory of gravitation (no field quantisation). The interaction is introduced by embedding the quantum mechanics of the otherwise unaffected (i.e. free) spin-1/2 particle in the given curved space-time of the 3-flat expanding Robertson-Walker universe. The metric acts thereby as an external field. The corresponding Hilbert space formalism is established in interpreting the generally covariant theory of the Dirac field in the Riemann space in question as the Dirac representation of the spin-1/2 particle in the Schrödinger picture. The evolution operator is then extracted out of the general relativistic Dirac equation, while contractions of the symmetric energy momentum tensor with the tetrad vectors of the reference system lead to the operators of energy, linear momentum and total angular momentum. The temporal behaviour of the corresponding expectation values is calculated.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.