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Journal of Applied Physics

Anomalous spin-wave excitations in a one-dimensional Dzyaloshinski–Moriya antiferromagnet

Qing Xia, Peter S. Riseborough

Published May 1, 1990• 6 citations
Publisher

Abstract

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.

DOI
10.1063/1.345856

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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 study the dispersion of magnetic excitations in a Heisenberg antiferromagnetic chain of spin S=1 with exchange J and single-ion anisotropy D. Chains of length up to 18 sites are studied by a Lanczo\ifmmode\ddot\else\textasciidieresis\fi{}s method. For the Haldane phase DDc{\mathit{D}}_{\mathit{c}}Dc​\ensuremath{\approxeq}J we show that the gap at zero momentum and Sz{\mathit{S}}^{\mathit{z}}Sz=1 is given by the sum of the gaps in the sectors Sz{\mathit{S}}^{\mathit{z}}Sz=1 and Sz{\mathit{S}}^{\mathit{z}}Sz=0 at momentum \ensuremath{\pi}. The transition region near D=J is likely to be reduced to an isolated point. Large-D perturbation theory is smoothly recovered as soon as D>2J. We discuss the implications for experiments on Ni(C2{\mathrm{C}}_{2}C2​H8{\mathrm{H}}_{8}H8​N2{\mathrm{N}}_{2}N2​)2{)}_{2})2​NO2{\mathrm{NO}}_{2}NO2​ClO4{\mathrm{ClO}}_{4}ClO4​ (NENP) as well as CsFeBr3{\mathrm{CsFeBr}}_{3}CsFeBr3​.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
Dzyaloshinskii–Moriya (DM) interactions cause many interesting physical features, such as topologically nontrivial magnetic skyrmions and chiral domain walls. These interactions become more pronounced in low-dimensional systems. We investigated a one-dimensional Heisenberg spin-1/2 chain with an asymmetric DM interaction. The results show that, upon applying a nonzero DM interaction, the Néel ground state transitions to a spin chiral phase. Moreover, using the mean-field approximation, we obtain the dispersion of the energy spectrum, from which the z-axis spin chirality is calculated as a function of the strength of the DM interaction for low-lying excitations. The results indicate that the DM interaction facilitates chirality for Dz ≤ J and induces a spin-gapped chiral state.