Excited states of quasi-one-dimensional hexagonal quantum antiferromagnets

Abstract

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.

Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

“…Hence, the longitudinal excitation states in antiferromagnets are constructed by the S z spin operators, contrast to the transverse spin operators S ± of the magnon states in Anderson's SWT [1]. Our preliminary calculation for the two dimensional triangular model [25] have been extended to the quasi-1D Hexagonal structures of CsNiCl 3 and RbNiCl 3 , where we find that our numerical results for the energy gap values at the magnetic wavevector are in good agreement with experimental results after inclusion of the high-order contributions in the large-s expansion [26]. In this article, we extend similar high-order calculations to the bipartite antiferromagnetic systems where the long-ranged order is collinear [27].…”

“…In this paper we have extended our high-order calculations for the longitudinal modes in the hexagonal quantum antiferromagnetic systems [26] to a number of bipartite systems, including the the quasi-1D compound KCuF 3 where good agreement in the minimum energy gap is found between the experimental result and our estimate after inclusion of the high-order contributions.…”

“…For completeness, in Sec. VI we include our earlier analysis [26] for the quasi-1D hexagonal systems where there are a number of experimental results for comparison. In Sec.…”

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

“…In this theory the longitudinal excitations are identified as the collective modes of the magnon-density waves, and the corresponding wave functions are constructed by employing the magnon-density operator S z in similar fashion to Feynman's theory on the low-lying excited states of the helium-4 superfluid where the particle density operator is used [40]. In our earlier calculations for the quasi-1D hexagonal structures of CsNiCl 3 and RbNiCl 3 and tetragonal structure of KCuF 3 , we find that, after the inclusion of the higher-order contributions from the quartic terms in the large-s expansion, the energy gap values at the magnetic wavevector are in good agreement with experimental results [41,42].…”

“…Our results show a significant reduction on the energy spectra due to the high order corrections. We also examine the cubic term contribution to the energy spectrum correction for the quasi-1D hexagonal systems of CsNiCl 3 and RbNiCl 3 , not considered in our earlier study [41]. We find that in these systems the cubic term contribution is negligible, mainly due to the very weak coupling on the triangular planes of the systems.…”