Primakoff Transformation Research Articles

Solitons in the Two-Dimensional Antiferromagnetic Heisenberg Model**The project supported in part by National Natural Science Foundation of China

An effective Hamiltonian of the two-dimensional antiferromagnetic Heisenberg model is derived by using the Holstein–Primakoff transformation. Three nonlinear coupled partial equations of motion are obtained. In the long-wavelength approximation, these equations, are reduced to the envelope function equations by the method of multiple scales. The amplitude functions satisfy the nonlinear Schrödinger equation. Introducing an inverse scattering transformation, the single-, two- and multi-soliton solutions in the two-dimensional antiferromagnetic Heisenberg model are investigated.

Green's Function Theory of the t- JModel

Within the framework of the supergroup theory and by making use of the general Holstein–Primakoff transformation, we set up an infinite hierarchy of equations of motion in the Green's functions for the t- Jmodel. A physical criterion involving self-consistency of the decoupling is presented. A Green's function method for the t- Jmodel, approximately valid through the entire temperature range, is given for low doping case. At low temperatures, the sublattice magnetization is in good agreement with the neutron scattering experiments in the high-temperature superconductors. The Néel temperatures and features at the antiferromagnetic-metalic phase transition region are obtained by taking into account the doping effect.

Non-linear spin-wave spectra in anisotropic magnetic superlattices

We present a theory for the dispersion relation and non-linear processes of spin-waves in a superlattice made up of two Heisenberg ferromagnets. Our calculations are carried out for the exchange-dominated regime, stressing the contribution of the surface modes. We consider the ferromagnetic materials described by a Heisenberg Hamiltonian, with the inclusion of both the uniaxial and non-uniaxial components of the single-ion anisotropy. Our theoretical model is based on the Holstein–Primakoff transformation to boson operators, while a Green function formalism with Feynman diagrams is employed as a perturbation theory to calculate the non-linear processes.

Spin waves at low temperatures in two-sublattice Heisenberg ferromagnets and ferrimagnets with different sublattice anisotropies

The Hamiltonian for two-sublattice Heisenberg ferromagnets and ferrimagnets with different sublattice anisotropies, which is applicable for rare-earth - transition-metal (R - T) intermetallics, is established. In order to study spin-waves in easy plane or easy cone configuration, a transformation of spin-vector coordinates is performed by rotating the quantization axis frame by Eulerian angles and accordingly the Hamiltonian. Spin-wave spectra at low temperatures of the present system are determined by performing the standard Holstein - Primakoff transformation and a four-step diagonalizing procedure consisting of two coupled Cullen transformations, an extended Bogoliubov transformation, two independent Bogoliubov transformations and two independent Holstein - Primakoff transformations. The results for the ground states of the easy axis, the easy plane and the easy cone configurations are compared with those obtained by the mean-field theory. The border lines between the different spin structures are derived in either the pure classical limit or the large-exchange limit. Continuous transitions, accompanied with the continuous change of the angle between the averaged sublattice magnetizations, are found in both cases. It is found that splittings of the spin-wave spectra of the two-sublattice Heisenberg ferromagnets or ferrimagnets exist. A gap can appear in the spin-wave spectra, depending on the competition among the exchange and the anisotropies. Other physical properties, such as sublattice magnetization and specific heat, are discussed also.

Correlated Holstein–Primakoff Transformation for Correlated Spin Coherent State

We show that by introducing the two-mode correlated Holstein–Primakoff transformation the correlated spin coherent state can be identified as a two-mode correlated binomial state. This fact can be used to describe populations on the three levels of an assembly of identical atoms.

Spin Wave Spectra of Ferromagnetic Superlattice with Antiparallel Magnetization11This project supported by National Natural Science Foundation of China

In this paper, by using the Holstein–Primakoff and Bogoliubov transformation, the spin wave spectra of ferromagnetic/nonmagnetic superlattice with antiparallel magnetizations between the neighboring ferromagnetic films are studied. The effects of some magnetic parameters on the spin wave spectra are discussed in detail.

Interacting Boson Approach to the Low-Dimensional Quantum Antiferromagnets: a Variational Monte–Carlo Study11This project supported by National Natural Science Foundation of China

We present a spin- antiferromagnetic Reisenberg model in an interacting boson representation exactly by using modified Holstein–Primakoff transformation. For interacting boson systems on one-dimensional linear chains and square lattices, we perform Monte–Carlo calculations using the well-established Jastrow-type trial wavefunction. We find that the ground state energies and spin correlations agree well with other numerical and theoretical results.

Solitary Excitations in Antiferrornagnets AFeBr311The project supported by National Natural Science Foundation of China

Introducing the Holstein–Primakoff transformation, the coherent-state ansatz and the time-dependent variation principle, we obtain two partial differential equations of motion. Employing the method of multiple scales, we reduce these equations into the envelope function equations and force the amplitude function to satisfy a nonlinear Schrödinger equation. Using the inverse-scattering transformation, we obtain the single-, two- and N-soliton solutions and discuss the gap soliton in antiferromagnets AFeBr3.

Studies On Magnetic Configurations In Multilayers by A Quantum Spin Model

ABSTRACTA method based on the variation of the magnetization direction of each layer and Holstein- Primakoff transformation is presented to estimate the magnetization configuration in a superlattice of quantum ferromagnetic system with an interface between perpendicular and in-plane easy-axis layers. Numerical results on the magnetization configurations under different applied magnetic fields, critical field, and critical anisotropic parameter are given.

Holstein–Primakoff Boson Realization for the Hydrogen Atom11The project supported by the Foundation of the Ph. D. Directing Programme of Chinese Universities.

We apply the Holstein–Primakoff transformation to the orbital angular momentum and the Runge–Lenz operators of a hydrogen atom to study its classical Kepler's problem. In this way the classical Kepler's frequency can be directly obtained without introducing Schwinger's boson realization and boson coherent states.

The Holstein Primakoff transformation in the generation of a squeezed field by collective atomic states

The Dicke hamiltonian of a single mode cavity interacting with a collective atomic state is here approximated by means of the Holstein Primakoff transformation. We thus obtain analytical solutions for the time evolution of the state and for the variances of the field which are valid in the lower range of energy. The squeezing obtained depends on the nature of the initial state (atomic or field coherent state). In both cases, for small times, it increases with time and exhibits oscillations which depend on the Rabi frequency. However only the initial field coherent state may generate a squeezed vacuum state.

Dyson Maleev transformation in ferromagnets with single ion planar anisotropy

We show that the Dyson Maleev (DM) transformation can be applied to the Heisenberg ferromagnet with single ion planar anisotropy, although the resulting bilinear part of the bosonic equivalent normally ordered Hamiltonian is not hermitian. With respect to the approaches adopted up to this moment, that is, the Holstein Primakoff (HP) transformation and the matching matrix elements (MME) method, the DM transformation offers relevant advantages because it generates a finite number of interaction potentials, so we are able to obtain the second-order perturbation contributions of the excitation energy, a practically impossible result to get in the HP and MME frame. In this communication we discuss the problem and show the main results; details of the very long, cumbersome calculations will be given elsewhere.

Bose operator expansions of tensor operators in the theory of magnetism. II

Using a method of matching corresponding matrix elements, a hermitian Bose-operator expansion of tensor operators of arbitrary rank which transforms all kinematic effects into dynamical interactions between Bose particles is derived. It is shown that the method is a generalization of the Holstein- Primakoff transformation of the angular momentum components. Tables are given for the Racah operators of rank k up to k=8 in terms of angular momentum operators and in terms of Bose operators. A similar table is given for the Stevens operators for even k up to k=6.

Bose-operator expansions of tensor operators in the theory of magnetism

Using a method of matching corresponding matrix elements, a hermitian Bose-operator expansion of tensor operators of arbitrary rank which transforms all kinematic effects into dynamical interactions between Bose particles is derived. It is shown that the method is a generalization of the Holstein- Primakoff transformation of the angular momentum components. Tables are given for the Racah operators of rank k up to k=8 in terms of angular momentum operators and in terms of Bose operators. A similar table is given for the Stevens operators for even k up to k=6.

On the uncertainty relation in the coherent spin-state representation

The product ( delta sx)2( delta sy)2 is computed where ( delta sx,y)2=(sx,y2)-(sx,y)2; averaging is performed in the coherent spin-state representation given by Radcliffe (1971). After applying the Holstein- Primakoff transformation s-=(2s)12/aDagger , s+=(2s)12/a and mu = alpha /(2s)12/, and putting s to infinity one proceeds from Radcliffe space into the Glauber space. After this procedure the product ( delta sx)2( delta sy)2 becomes ( delta x)2( delta p)2. Using the Jackiw equation it is shown that the function mod mu =0> is the only one which minimizes the uncertainty product, for every s.

Boson Representations of the Heisenberg Model

Maleev's transformation to boson operators is often used to recover Dyson's result for the excitation spectrum of a Heisenberg ferromagnet. However, we show that a simple use of the Holstein–Primakoff transformation is adequate to obtain the same excitation spectrum. We have used a Zubarev-type Green function approach in which no decoupling approximation is needed. However, an approximation for the polarization operator is used.