Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1105.2259 · Physical Review Letters

Theory of Raman Scattering in One-Dimensional Quantum Spin- 12 Antiferromagnets

Masahiro Sato, Hosho Katsura, Naoto Nagaosa

Published Jun 4, 2012• 10 citations
arXivHTMLPDF

Abstract

We study theoretically the Raman-scattering spectra in the one-dimensional (1D) quantum spin-1/2 antiferromagnets. The analysis reveals that their low-energy dynamics is exquisitely sensitive to various perturbations to the Heisenberg chain with nearest-neighbor exchange interactions, such as magnetic anisotropy, longer-range exchange interactions, and bond dimerization. These weak interactions are mainly responsible for the Raman scattering and give rise to different types of spectra as functions of frequency, temperature, and external field. In contrast to the Raman spectra in higher dimensions in which the two-magnon process is dominant, those in 1D antiferromagnets provide much richer information on these perturbations.

DOI
10.1103/physrevlett.108.237401

Related papers

Magnetic Raman Scattering from 1D Antiferromagnets

Rajiv R. P. Singh, Peter Prelovšek, B. Sriram Shastry

We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor ( ${J}_{1}$) and second-neighbor ( ${J}_{2}$) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$. We find that the low- $T$ Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at $T>{J}_{1}$ the spectra are narrower and peaked at low frequencies. The experimental spectra for ${\mathrm{CuGeO}}_{3}$ are discussed in light of our calculations.

Physical Review Letters•Nov 4, 1996•12 citations

Inelastic light scattering in low-dimensional spin systems

Kwang‐Yong Choi

In this work diverse results obtained from a number of low-dimensional quantum spin systems using Raman spectroscopy have been presented. The main motivation of this thesis is to hunt for new types of elementary excitations which may be present in low-dimensional spin systems with exotic spin topology. The studied systems can be on the one hand characterized by the formation of spin dimers which originate from a special spin topology like ACuCl3 (A=Tl, K), LiCu2O2, and SrCu(BO3)2. On the other hand, the system such as K2V3O8 and Cu2Te2O5X2 (X=Br,Cl) is dominated by quantum fluctuations due to reduced dimensionalilty. A powerful tool for studying low-dimensional spin systems is Raman spectroscopy which is sensitive to nearly all possible types of collective excitations as well as the interplay among them. In particular, magnetic light scattering can provide information about exchange paths and coupling constants, spinon excitations, spin gaps, and triplet-triplet interactions. The main results are summarized as follows; (i) the observation of a coherent coexistence of long-rang order and dimerized state in the frustrated spin chain system LiCu2O2, (ii) the presence of three-magnon scattering and dynamic spin-phonon coupling in the three-dimensional coupled spin dimer systems ACuCl3 (A=Tl, K), (iii) anomalous low-energy excitations including two-magnon scattering and electronic/orbital excitations in the two-dimensional Heisenberg antiferromagnetic system K2V3O8, (iv) the observation of inter-plane soft mode and a coupling of spin to soft mode in the quasi two-dimensional orthogonal dimer system SrCu(BO3)2, and (v) the existence of longitudinal magnons in the spin tetrahedra system Cu2Te2O5X2 (X=Br,Cl).

•Jan 1, 2003•0 citations

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

Takashi Inoue, Shoji Yamamoto

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.

arXiv:2604.25401•Journal of the Physical Society of Japan•Jun 1, 2026•0 citations

Magnetic Raman Scattering in Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets: Spectral Shape Anomaly and Magnetostrictive Effects

Franco Nori, Roberto D. Merlin, Stephan Haas +2 more

We calculate the Raman spectrum of the two-dimensional spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with Raman scattering experiments on various high- ${T}_{c}$ precursors, such as ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.2}$. In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden ${A}_{1g}$ scattering.

arXiv:cond-mat/9505012•Physical Review Letters•Jul 17, 1995•42 citations

Raman study of one-dimensional spin fluctuations in the spin-1 Heisenberg-chain compound Y2 BaNiO5 : Contrast with simple expectations

P. E. Sulewski, S‐W. Cheong

Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline ${\mathrm{Y}}_{2}$${\mathrm{BaNiO}}_{5}$, a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.

Physical review. B, Condensed matter•Feb 1, 1995•10 citations

Two-magnon Raman scattering in a Mott-Hubbard antiferromagnet

Saurabh Basu, Avinash Singh

A perturbation-theoretic diagrammatic scheme is developed for systematically studying the two-magnon Raman scattering in a Mott-Hubbard antiferromagnet. The fermionic structure of the magnon interaction vertex is obtained at order-$\frac{1}{\mathcal{N}}$ level in an inverse-degeneracy expansion, and the relevant two-magnon propagator is obtained by incorporating magnon interactions at a ladder-sum level. Evaluation of the magnon interaction vertex in the large-$U$ limit yields a nearest-neighbor instantaneous interaction with interaction energy $\ensuremath{-}J$. Application of this approach to the intermediate-$U$ regime, which is of relevance for cuprate antiferromagnets, is also discussed. Incorporating the zero-temperature magnon damping, which is estimated in terms of quantum spin fluctuations, the two-magnon Raman scattering intensity is evaluated and compared with experiments on ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$.

Physical review. B, Condensed matter•Sep 1, 1996•6 citations
We study theoretically the Raman-scattering spectra in the one-dimensional (1D) quantum spin-1/2 antiferromagnets. The analysis reveals that their low-energy dynamics is exquisitely sensitive to various perturbations to the Heisenberg chain with nearest-neighbor exchange interactions, such as magnetic anisotropy, longer-range exchange interactions, and bond dimerization. These weak interactions are mainly responsible for the Raman scattering and give rise to different types of spectra as functions of frequency, temperature, and external field. In contrast to the Raman spectra in higher dimensions in which the two-magnon process is dominant, those in 1D antiferromagnets provide much richer information on these perturbations.
We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor ( J1{J}_{1}J1​) and second-neighbor ( J2{J}_{2}J2​) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for J2=0{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0J2​=0 and J2=1/2{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2J2​=1/2. We find that the low- TTT Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at T>J1T>{J}_{1}T>J1​ the spectra are narrower and peaked at low frequencies. The experimental spectra for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ are discussed in light of our calculations.
In this work diverse results obtained from a number of low-dimensional quantum spin systems using Raman spectroscopy have been presented. The main motivation of this thesis is to hunt for new types of elementary excitations which may be present in low-dimensional spin systems with exotic spin topology. The studied systems can be on the one hand characterized by the formation of spin dimers which originate from a special spin topology like ACuCl3 (A=Tl, K), LiCu2O2, and SrCu(BO3)2. On the other hand, the system such as K2V3O8 and Cu2Te2O5X2 (X=Br,Cl) is dominated by quantum fluctuations due to reduced dimensionalilty. A powerful tool for studying low-dimensional spin systems is Raman spectroscopy which is sensitive to nearly all possible types of collective excitations as well as the interplay among them. In particular, magnetic light scattering can provide information about exchange paths and coupling constants, spinon excitations, spin gaps, and triplet-triplet interactions. The main results are summarized as follows; (i) the observation of a coherent coexistence of long-rang order and dimerized state in the frustrated spin chain system LiCu2O2, (ii) the presence of three-magnon scattering and dynamic spin-phonon coupling in the three-dimensional coupled spin dimer systems ACuCl3 (A=Tl, K), (iii) anomalous low-energy excitations including two-magnon scattering and electronic/orbital excitations in the two-dimensional Heisenberg antiferromagnetic system K2V3O8, (iv) the observation of inter-plane soft mode and a coupling of spin to soft mode in the quasi two-dimensional orthogonal dimer system SrCu(BO3)2, and (v) the existence of longitudinal magnons in the spin tetrahedra system Cu2Te2O5X2 (X=Br,Cl).
We study first-order (single-magnon) inelastic light scatterings in spin-12\frac{1}{2}21​ 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.
We calculate the Raman spectrum of the two-dimensional spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with Raman scattering experiments on various high- Tc{T}_{c}Tc​ precursors, such as La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and YBa2Cu3O6.2{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.2}YBa2​Cu3​O6.2​. In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden A1g{A}_{1g}A1g​ scattering.
Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline Y2{\mathrm{Y}}_{2}Y2​BaNiO5{\mathrm{BaNiO}}_{5}BaNiO5​, a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.
A perturbation-theoretic diagrammatic scheme is developed for systematically studying the two-magnon Raman scattering in a Mott-Hubbard antiferromagnet. The fermionic structure of the magnon interaction vertex is obtained at order-1N\frac{1}{\mathcal{N}}N1​ level in an inverse-degeneracy expansion, and the relevant two-magnon propagator is obtained by incorporating magnon interactions at a ladder-sum level. Evaluation of the magnon interaction vertex in the large-UUU limit yields a nearest-neighbor instantaneous interaction with interaction energy $\ensuremath{-}J$. Application of this approach to the intermediate-UUU regime, which is of relevance for cuprate antiferromagnets, is also discussed. Incorporating the zero-temperature magnon damping, which is estimated in terms of quantum spin fluctuations, the two-magnon Raman scattering intensity is evaluated and compared with experiments on La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{O}}_{4}O4​.