Excited states of the quasi-one-dimensional hexagonal quantum antiferromagnets

TL;DR

This paper studies the excited states of quasi-one-dimensional hexagonal quantum antiferromagnets, focusing on both transverse and longitudinal modes, and compares theoretical energy gaps with experimental data, revealing good agreement.

Contribution

It introduces a spin-wave theory based on the one-boson method to analyze longitudinal modes in non-collinear antiferromagnets, extending previous phenomenological approaches.

Findings

Identified two longitudinal modes due to non-collinear order.

Calculated energy gaps consistent with experimental results.

Demonstrated the importance of higher-order contributions.

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 non-integer spin quantum numbers, and we find good agreement after the higher-order contributions are included in our calculations.