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arXiv:2604.25401 · Journal of the Physical Society of Japan

Raman Characterization of Two-Dimensional Quasiperiodic Antiferromagnets on Various Lattices: Spin–Orbit Mechanism

Takashi Inoue, Shoji Yamamoto

Published Jun 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We study first-order (single-magnon) inelastic light scatterings in spin-$\frac{1}{2}$ two-dimensional quasiperiodic antiferromagnets in comparison with those emergent on periodic lattices. Unlike second-order (two-magnon) Raman scatterings based on an exchange interaction between neighboring spins, the present observations involve an indirect electric-dipole coupling which proceeds through a spin-orbit interaction. We discuss the nearest-neighbor antiferromagnetic XXZ Hamiltonian on various quasiperiodic and periodic bipartite lattices. The first-order spectra, of our present interest, consist only of rotation-invariant and mirror-symmetric magnons, while the second-order ones cannot select any particular magnon. With the exchange anisotropy moving away from the Ising limit toward the Heisenberg isotropic point, every initial delta-function peak bifurcates or divides into more in each individual manner on quasiperiodic lattices, while it remains singly peaked all the way on periodic lattices. Such splittings depend on how many types of isocoordinated sites for each coordination number and relative positions between those of the same type. A perpendicular-space representation of the first-order Raman spectrum serves as a fingerprint of each quasiperiodic tiling.

DOI
10.7566/jpsj.95.064706

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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.
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