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Journal of Physics Condensed Matter

Heisenberg Hamiltonian with a Dzyaloshinski-Moriya interaction

Indrani Bose, Uma Bhaumik

Published Nov 28, 1994• 11 citations
Publisher

Abstract

The spin- 1/2 ferromagnetic Heisenberg Hamiltonian with a Dzyaloshinski-Moriya interaction and in the presence of a strong magnetic field is studied in one dimension. Using the exact Bethe ansatz analysis, the excitation spectrum of one- and two-magnon states is derived. It is further shown that in certain parameter regimes the two-magnon bound state exists in the full range of allowed values of the centre-of-mass momentum wavevector k.

DOI
10.1088/0953-8984/6/48/020

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The spin- 1/2 ferromagnetic Heisenberg Hamiltonian with a Dzyaloshinski-Moriya interaction and in the presence of a strong magnetic field is studied in one dimension. Using the exact Bethe ansatz analysis, the excitation spectrum of one- and two-magnon states is derived. It is further shown that in certain parameter regimes the two-magnon bound state exists in the full range of allowed values of the centre-of-mass momentum wavevector k.
The dynamics of a one-dimensional Heisenberg antiferromagnet with a small Dzyaloshinski–Moriya component to the exchange interaction is considered. The spin rotational invariance within the easy plane is broken by the application of a weak magnetic field in the easy plane. The nature of the spin-wave excitations of the quantum spin system is investigated, and pronounced anomalies in the single-spin-wave spectrum at fields comparable to the anisotropy in the exchange interaction are found. These anomalies are of quantum character and are related to the resonance between the single-spin-wave and the two-spin-wave excitations. The implications for the two-spin-wave bound states are discussed.
We consider a two-magnon systems in an ν-dimensional isotropic non-Heisenberg ferromagnet with spin value S = 3/2 and nearest-neighbor interactions. Spectrum and bound states (BS) of the system for all values of full quasi-momentum Λ, and for arbitrary value of lattice dimensionality ν, and for all values of Hamiltonian parameters are investigated. We show that (i) for arbitrary ν ≥ 2 and for full quasi-momentum in the form Λ = (Λ1; Λ2; … ;Λν) = (Λ0;Λ0; …; Λ0) the change of energy spectrum of the system is similar to that observed in the case of ν = 1. In this case the operator [Formula: see text] with J + J1 - 23J2 ≠ 0 has only one additional BS. (ii) The energy z of this additional BS is degenerate ν - 1 times. (iii) If Λ ≠ (Λ0;Λ0;…;Λ0), we show the existence no more 2ν + 1 bound states in the system in ν-dimensional lattice.
Quantum entanglement is one of the most important measures of quantum correlations. Using group-theoretical approach we found a family of four nine-parameter quantum states for the two-spin-1/2 Heisenberg system in an external magnetic field and with multiple components of Dzyaloshinsky-Moriya (DM) and Kaplan-Shekhtman- Entin-Wohlman-Aharony (KSEA) interactions. Exact analytical formulas are derived for the entanglement of formation for the quantum states found. In the proceeding, the family of found states and the structure of interactions in them are discussed.
The influence of a magnetic impurity on the elementary excitation spectrum of a two-dimensional Ising ferromagnet is investigated in a low transverse magnetic field. It is shown that in the case of a “ferromagnetic” impurity in a matrix of spin 1/2, from one to three local energy levels can be split off from the lower edge of the continuous spectrum of one-magnon states where the conditions for their existence impose quite strict constraints on the spin-Hamiltonian parameters. Three distinct spin configurations can be realized in the presence of an “antiferromagnetic” impurity in the crystal in the ground state. Single-magnon states of a ferromagnet are considered for those values of the spin-Hamiltonian parameters when two of them are realized. It is shown that from one to six local levels above or below the continuous spectrum band can appear, and their distance from the band edge can substantially exceed its width. Quasilocal energy levels originating within the continuous spectrum of the single-magnon states are also investigated.