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Ferroelectrics

Microscopic derivation of domin walls

A. R. Bishop, Eytan Domany, JAMES A. KRUMHANSL

Published Jan 1, 1977• 24 citations
Publisher

Abstract

A variational calculation yields an eigenstate representing a domain wall-type solution for various quantum-mechanical spin models. Heisenberg Hamiltonians with local and exchange anisotropy, and an Ising model in a transverse field (including its critical regime) are discussed in detail. The domain walls are viewed as localized solutions of non-linear equations. The extent to which the results for the transverse field Ising model may be mapped on to a currently interesting “double well” anhurmonic lattice problem are analysed.

DOI
10.1080/00150197708237153

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Within the classical and quantum S= 1 / 2 versions of the one-dimensional Ising model in a transverse field non-linear domain-wall-like excitations are studied. For the quantum case a domain wall (DW) wavefunction is constructed from the first (improper) excitation band. Various one-DW expectation values are then calculated. In particular, it is shown that the proposed DW wavefunction indeed yields the expected stationary-wall-like profile for the (S l z ) expectation value. Results are compared with the ones obtained for the classical model and used to analyse the quantum-classical correspondence of domain walls in both models. The extension to non-stationary quantum DW is briefly discussed.

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Domain-Wall Excitations in an Ising-Like Antiferromagnetic Chain under a Transverse Magnetic Field

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We study effects of a transverse magnetic field on the properties of the one-dimensional spin-1/2 Ising-like antiferromagnet. In order to emphasize the relevant role of domain walls between opposite antiferromagnetic domains, the spin Hamiltonian is exactly mapped to the interacting fermion Hamiltonian, via the dual transformation as well as the Jordan-Wigner transformation. Within the generalized Hartree-Fock approximation, we find that the excitation spectrum exhibits characteristic features, which are explained as a result of the different roles of the transverse field and of the transverse components of the exchange interactions in the propagation of the domain wall. At a critical field where the excitation gap vanishes, a ground-state phase transition is found to take place in the same manner as that in the transverse Ising model. In addition, we discuss the relevance of our magnetization curve with regard to experimental data in CsCoCl 3 .

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Domain-wall excitations in the spin-(1)/(2) X X Z linear chain: A new variational approach

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The linear chain XXZ spin- (1)/(2) Hamiltonian is mapped onto a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The domain-wall Hamiltonian is solved within the simplest Hartree–Fock approximation with results in very good agreement with the exact solution in the antiferromagnetic regime. The location of ordered and disordered (critical) phases is correct and low-lying excitations are well described and easily interpreted in terms of domain walls. Our domain-wall version of the original Hamiltonian is shown to provide the natural framework for a physical understanding of this system in the antiferromagnetic regime.

Journal of Applied Physics•May 1, 1990•0 citations
A variational calculation yields an eigenstate representing a domain wall-type solution for various quantum-mechanical spin models. Heisenberg Hamiltonians with local and exchange anisotropy, and an Ising model in a transverse field (including its critical regime) are discussed in detail. The domain walls are viewed as localized solutions of non-linear equations. The extent to which the results for the transverse field Ising model may be mapped on to a currently interesting “double well” anhurmonic lattice problem are analysed.
Within the classical and quantum S= 1 / 2 versions of the one-dimensional Ising model in a transverse field non-linear domain-wall-like excitations are studied. For the quantum case a domain wall (DW) wavefunction is constructed from the first (improper) excitation band. Various one-DW expectation values are then calculated. In particular, it is shown that the proposed DW wavefunction indeed yields the expected stationary-wall-like profile for the (S l z ) expectation value. Results are compared with the ones obtained for the classical model and used to analyse the quantum-classical correspondence of domain walls in both models. The extension to non-stationary quantum DW is briefly discussed.
Nonlinear excitations in the Ising model in a transverse field or an equivalent Frenkel-exciton model for a system of two-level atoms are studied by using a method of diagonal coherent-state representation. It is shown that if the ratio of the Ising interaction to a transverse-field strength exceeds a certain critical value, stationary coherent states giving the ground state and excited states of the model Hamiltonian are characterized by two degenerate structures resulting from spatially uniform coherent states and static domain-wall type excitations, respectively. Particular solutions for the time evolution of spin operators corresponding to atomic polarization are then studied. It is shown that moving domain-wall solutions or moving solitary-wave solutions can exist under certain conditions.
Dynamics and the approximate thermodynamical properties of the classical Ising model in a transverse field (CIMTF) are studied. This is done by elucidating a close correspondence of the CIMTF to a nonlinear lattice field in which each atom, while coupled harmonically with its neighbours, sits on on-site anharmonic potential. It is shown that when the ratio of the Ising interaction to a transverse field-strength exceeds a certain critical value, the on-site potential is of double-well type with saturable nonlinearity. Domain wall modes and magnon modes in continuous one-dimensional CIMTF are studied for both systems to substantiate the correspondence. By exploiting this, a brief study is made on the approximate properties of the free energy and of the dynamical structure factor S ( k ,ω) of longitudinal spin fluctuations of the CIMTF. These quantities are shown to be composed of two contributions, one from domain-wall modes and the other from magnon modes, which manifest themselves as a central peak and side peaks in S ( k ,ω), respectively.
We study effects of a transverse magnetic field on the properties of the one-dimensional spin-1/2 Ising-like antiferromagnet. In order to emphasize the relevant role of domain walls between opposite antiferromagnetic domains, the spin Hamiltonian is exactly mapped to the interacting fermion Hamiltonian, via the dual transformation as well as the Jordan-Wigner transformation. Within the generalized Hartree-Fock approximation, we find that the excitation spectrum exhibits characteristic features, which are explained as a result of the different roles of the transverse field and of the transverse components of the exchange interactions in the propagation of the domain wall. At a critical field where the excitation gap vanishes, a ground-state phase transition is found to take place in the same manner as that in the transverse Ising model. In addition, we discuss the relevance of our magnetization curve with regard to experimental data in CsCoCl 3 .
The linear chain XXZ spin- (1)/(2) Hamiltonian is mapped onto a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The domain-wall Hamiltonian is solved within the simplest Hartree–Fock approximation with results in very good agreement with the exact solution in the antiferromagnetic regime. The location of ordered and disordered (critical) phases is correct and low-lying excitations are well described and easily interpreted in terms of domain walls. Our domain-wall version of the original Hamiltonian is shown to provide the natural framework for a physical understanding of this system in the antiferromagnetic regime.