Abstract
Based on our recently proposed magnon-density-waves using the microscopic many- body 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.
Highlights
The dynamics of the two-dimensional (2D) and threedimensional (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 with its density given by the quantum correction to the classical Neel order [1,2,3]
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 find good agreement after the higher-order contributions are included in our calculations
The observation of an energy gap for the quasi1D compound CsNiCl3 at low temperature in 1986 generated much theoretical interest [6]. This energy gap was initially explained by a uniaxial single-ion anisotropy but it is widely accepted that the gapped excited state belongs to longitudinal excitation modes, first proposed by Affleck [in the quasi-1D hexagonal antiferromagnetic compounds of the ABX3-type with both spin quantum number s = 1 CsNiCl3 and RbNiCl3 [15, 16]
Summary
The dynamics of the two-dimensional (2D) and threedimensional (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 Neel order [1,2,3]. The key question is whether or not the longitudinal modes survive in present of the long-ranged order and, if the answer is yes, how we describe them in general terms In this regard, the observation of an energy gap for the quasi1D compound CsNiCl3 at low temperature in 1986 generated much theoretical interest [6]. VII we conclude this article by a summary and a discussion of a possible longitudinal mode in a 2D square lattice model, relevant to the parent compound La2CuO4 of the high-Tc superconductors
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