Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.     

Thermal and magnetic properties of a ferrimagnetic nanoparticle with spin-3/2 core and spin-1 shell structure

Intensive Monte Carlo simulations based on standard Metropolis algorithm have been applied to investigate the phase diagrams of a ferrimagnetic cubic nanoparticle (nanocube) with a spin-3/2 core surrounded by a spin-1 shell layer with antiferromagnetic interface coupling. It has been shown that occupation of sites of particle core by spin-3/2 plays an important role on the shape of the phase diagrams. In addition, effects of the crystal field interaction as well as exchange interactions on the thermal and magnetic properties of the system have also been discussed in detail, and some interesting features have been observed for the temperature dependence of total magnetization curves of particle.     

Exact Green's function for rectangular potentials and its application to quasi-bound states

In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also generalizing and resuming results in the literature. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression. From the poles and residues of the Green's function the bound states eigenenergies and eigenfunctions with the correct normalization constant are obtained. In order to show the versatility of the method, an application of the Green's function approach to extract information of quasi-bound states in rectangular barriers, where the standard analysis of quantum amplitudes fail, is presented.     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

Spin compensation temperatures in the mean-field approximation of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system

The magnetic behaviors of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system on a square lattice are studied with the mean-field approximation (MFA) based on the Bogoliubov inequality for the free energy. A Landau expansion of the free energy in the order parameter is also described in this work. In particular, we investigate the effect of a single-ion anisotropy on the compensation phenomenon.     

Selftuned massive spin-2

We calculate the cubic order terms in a covariant theory that gives a nonlinear completion of the Fierz–Pauli massive spin-2 action. The resulting terms have specially tuned coefficients guarantying the absence of a ghost at this order in the decoupling limit. We show in this limit that: (1) The quadratic theory propagates helicity-2, 1, and helicity-0 states of massive spin-2. (2) The cubic terms with six derivatives – which would give ghosts on local backgrounds – cancel out automatically. (3) There is a four-derivative cubic term for the helicity-0 field, that has been known to be ghost-free on any local background. (4) There are four-derivative cubic terms that mix two helicity-0 fields with one helicity-2, or two helicity-1 fields with one helicity-0; none of them give ghosts on local backgrounds. (5) In the absence of external sources, all the cubic mixing terms can be removed by nonlinear redefinitions of the helicity-2 and helicity-1 fields. Notably, the helicity-2 redefinition generates the quartic Galileon term. These findings hint to an underlying nonlinearly realized symmetry, that should be responsible for what appears as the accidental cancellation of the ghost.     

Tensor formulation of spin-1 and spin-2 fields

Spin projection operators which constitute a resolution of the identity in the space of second rank tensor wave functions are constructed. These projectors are then used to establish Lagrangian quantum field theories for free massive particles with spin-1 (two equivalent formulations) and spin-2.     

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     

Exact eigenstates and magnetic response of spin-1 and spin-2 bose-einstein condensates

The exact eigenspectra and eigenstates of spin-1 and spin-2 Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEC, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlations among three bosons.     

Automated computation of spin- and colour-correlatedBorn matrix elements

I report on an implementation of an algorithm for the automated numerical calculation of spin- and colour-correlated Born matrix elements in QCD. These spin- and colour-correlated matrix elements are needed for NLO calculations in combination with the subtraction method. Both massless and massive quarks are considered. There are no restrictions on the number of external particles. As a trivial sub-case, the algorithm also applies to Born matrix elements without any correlations. These are sufficient for leading order calculations.     

Polarization of spin-1 particles in a uniform magnetic field

The exact solution of the Corben–Schwinger equations is obtained for spin-1 particles without an anomalous magnetic moment in a uniform magnetic field. The exact Hamiltonian in the Foldy–Wouthuysen representation is derived. The conservation of projections of the polarization operator onto four directions is proved. The approximate conservation of projections of this operator onto the horizontal axes of the cylindrical coordinate system is established. For spin-1 particles with the anomalous magnetic moment, the Hamiltonian in the Foldy–Wouthuysen representation is deduced within first order terms in the Planck constant. Dynamics of spin-1 particles with the anomalous magnetic moment and their spins in the strong uniform magnetic field are calculated.     

Acoustic spin-1 Weyl semimetal

The study of topological semimetals hosting spin-1 Weyl points(WPs) beyond Dirac points and WPs has attracted a great deal of attention. However, a spin-1 Weyl semimetal that exclusively possesses spin-1 WPs in a clean frequency window without being shadowed by any other nodal points is yet to be discovered. This study reports a spin-1 Weyl semimetal in a phononic crystal. Its spin-1 WPs are touched by two linear dispersions and an additional flat band and carry monopole charges(-2,0,2) or(2,0,-2) for the three bands from the bottom to the top. They result in double Fermi arcs, which occur between the first and second bands, as well as between the second and third bands. Further robust propagation is observed against the multiple joints and topological negative refraction of the acoustic surface arc wave. The results of this study create the basis for the exploration of the unusual properties of spin-1 Weyl physics on a macroscopic scale.     

Nematic order by disorder in spin-2 Bose-Einstein condensates

We show that quantum and thermal fluctuations in spin-2 Bose-Einstein condensates lift the accidental degeneracy of the mean-field phase diagram. Fluctuations select the uniaxial (square biaxial) nematic state for scattering lengths a4>a2 (a4相似文献   

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

Nonlinear massive spin-2 field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein’s gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called “(Helmholtz-)Jordan frame” and “Einstein frame.” In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.     

On energy-momentum tensors as sourcesof spin-2 fields

The improvement terms in the generalised energy-momentum tensor of Callan, Coleman and Jackiw can be derived from a variational principle if the Lagrangian is generalised to describe coupling between ‘matter’ fields and a spin-2 boson field. The required Lorentz-invariant theory is a linearised version of Kibble-Sciama theory with an additional (generally-covariant) coupling term in the Lagrangian. The improved energy-momentum tensor appears as the source of the spin-2 field, if terms of second order in the coupling constant are neglected.     

Thermodynamic properties of the mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies is solved exactly by means of a mapping to the spin-1/2 Ising chains with alternating transverse fields and the Jordan-Wigner transformation. Within this scheme, the thermodynamic quantities of this model are rigorously determined by a recursion formula derived for the partition function based on the reduced spin-1/2 transverse Ising model. The corresponding thermodynamic properties are calculated and discussed.     

Dynamic magnetic properties in the kinetic mixed spin-2 and spin-5/2 Ising model under a time-dependent magnetic field

We extend the recent paper [W. Jiang, V-C. Lo, B-D. Bai, J. Yang, Physica A 389 (2010) 2227-2233] to present a study, within a mean-field approach, the dynamic magnetic properties of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system, which corresponds the molecular-based magnetic materials AFe^IIFe^III(C₂O₄)₃ [ A=N(n-C_nH_2n+1)₄, n=3-5], by using the Glauber-type stochastic dynamics. This mixed Ising ferrimagnetic system is used on a layered honeycomb lattice in which Fe^II (S=5/2) and Fe^III (σ=2) occupy sites. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first-or second-order) phase transitions. We also present the dynamic phase diagrams and study the dynamic magnetic hysteresis loop behaviors of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system. The results are compared with some experimental and theoretical works and a good overall agreement is found.     

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.