Longitudinal Excitations in Triangular Lattice Antiferromagnets

2014

J. Phys.: Conf. Ser.

Abstract. Based on our recently proposed magnon-density-waves using the microscopic manybody approach, we investigate the longitudinal excitations in quantum antiferromagnets by including the second order corrections in the large-s expansion. The longitudinal excitation spectra for a general spin quantum number using the antiferromagnetic Heisenberg Hamiltonian are obtained for various spin lattice models. For bipartite lattice models, we find that the numerical results for the energy gaps for the longitudinal modes at q → 0 and the magnetic ordering wavevector Q are reduced by about 40-50 % after including the second order corrections. Thus, our estimate of the energy gaps for the quasi-one-dimensional (quasi-1D) antiferromagnetic compound KCuF3 is in better agreement with the experimental result. For the quasi-1D antiferromagnets on hexagonal lattices, the full excitation 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 find 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. We compare 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 also find good agreement after the higher-order contributions are included in our calculations. introductionThe dynamics of the two-dimensional (2D) and three-dimensional (3D) quantum antiferromagnetic systems with long-ranged order at low temperature can be considered as that of a dilute gas of weakly interacting spin-wave quasiparticles (magnons) with its density given by the quantum correction to the classical Néel order [1,2,3]. These magons are transverse modes with spin S = ±1. The longitudinal fluctuations with spin S = 0 present in these systems consist of the multi-magnon continuum [4]. The question concerning long-lived, well-defined longitudinal modes in quantum antiferromagnetic systems with long-ranged order remains open. This is our main focus in this paper.In case of the quantum antiferromagnetic systems without long-ranged order, the triplet excitation states (two transverse and one longitudinal) of the spin-1 Heisenberg chain with nonzero gap, first predicted by Haldane [5], are well known. This theoretical prediction of an energy gap separating the singlet ground state from the triplet excitation states has been confirmed experimentally in the quasi-1D antiferromagnetic compounds such as CsNiCl 3 and RbNiCl 3 of the spin-1 [6]. Some subsequent experimental investigations [7,6,8,9, 10] and theoretical calculations [11,12,13,14,3] also support Haldane's conjecture. In these experiments, the temperature is high enough so the quasi-1D systems have no long-ranged magnetic order and

Section: Hexagonal Quasi-1d Abx3-type Antiferromagnetic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

2014

J. Phys.: Conf. Ser.

“…We like to point out that, the calculations of both Eqs. (28) and (31) involve up to four-boson operators. We first discuss the general behaviors of the longitudinal spectrum of Eq.…”

Section: The Longitudinal Modes Of the Quasi-1d Hexagonal Antifementioning

confidence: 99%

“…I. In the other limit, ξ → ∞, the Hamiltonian is a pure triangular antiferromagnet with the quasi-gapped longitudinal modes as discussed in details in our previous paper [31] where we keep only the first order term in Eq. ( 28) in the large s-expansion, similar to the case of the square lattice model.…”

Section: The Longitudinal Modes Of the Quasi-1d Hexagonal Antiferroma...mentioning

confidence: 99%

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Excited states of quasi-one-dimensional hexagonal quantum antiferromagnets

2013

Phys. Rev. B

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We investigate 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 compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and noninteger spin quantum numbers, and we find good agreement after the higher-order contributions are included in our calculations.

The Effects of Three Magnons Interactions in the Magnon-Density Waves of Triangular Spin Lattices

2019

J Low Temp Phys

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We investigate the magnon-density waves proposed as the longitudinal excitations in triangular lattice antiferromagnets by including the cubic and quartic corrections in the large-s expansion. The longitudinal excitation spectra for the two-dimensional (2D) triangular antiferromagnetic model and quasi-one dimensional (quasi-1D) antiferromagnetic materials have been obtained for a general quantum spin number s. For the 2D triangular lattice model, we find a significant reduction (about 40 %) in the energy spectra at the zone boundaries due to both the cubic and quartic corrections. For the quasi-1D antiferromagnets, since the cubic term comes from the very weak couplings on the hexagonal planes, they make very little correction to the energy spectra, whereas the major correction contribution comes from the quartic terms in the couplings along the chains with the numerical values for the energy gaps in good agreement with the experimental results as reported earlier (Ref. 41). arXiv:1901.11007v2 [cond-mat.str-el]