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

Physical review. B, Condensed matter

Two-magnon Raman scattering in a Mott-Hubbard antiferromagnet

Saurabh Basu, Avinash Singh

Published Sep 1, 1996• 6 citations
Publisher

Abstract

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${\mathrm{O}}_{4}$.

DOI
10.1103/physrevb.54.6356

Related papers

Spin-wave spectral properties of the Mott-Hubbard antiferromagnet: The intermediate-coupling regime

Avinash Singh

Spectral properties of spin-wave excitations in the Mott-Hubbard antiferromagnet are studied in the intermediate-coupling regime, wherein extended-range spin couplings are present in the equivalent spin-1/2 Heisenberg model. A systematic expansion in powers of ${\mathit{t}}^{2}$/${\mathit{U}}^{2}$ is developed for the spin-wave propagator in the random-phase approximation, and its quantitative usefulness is investigated. In two dimensions the spin-wave density of states exhibits a peak structure, resembling the broadening effect of spin-wave damping. Implications for recent light-pair scattering experiments in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ wherein the complete spin-wave spectrum is accessible in principle, are discussed.

Physical review. B, Condensed matter•Sep 1, 1993•10 citations

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

Masahiro Sato, Hosho Katsura, Naoto Nagaosa

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.

arXiv:1105.2259•Physical Review Letters•Jun 4, 2012•10 citations

Fermionic structure of the magnon interaction vertex in quantum magnets

Avinash Singh

Fermionic structure of the spin-wave interaction vertex within the Hubbard-model representation of a quantum magnet is presented in a scheme that systematically preserves the spin-rotational symmetry and hence the Goldstone mode. We evaluate the diagrams contributing to the interaction vertex for the case of a quantum antiferromagnet in the strong-coupling limit. The exact cancellation of the leading-order contributions (of order U), as required by spin-rotational symmetry, is demonstrated.

Physical review. B, Condensed matter•Oct 1, 1993•0 citations

Raman scattering cross section of spin ladders

E. Orignac, R. Citro

The Raman scattering spectra from magnetic excitations in an antiferromagnetic spin-$\frac{1}{2}$ two leg ladder is investigated for weak and strong interladder coupling. In the first case, a cusp in the Raman intensity is obtained at a frequency twice the gap. In the second case, a peak at twice the gap replaces the cusp. We discuss the relevance of our calculation to recent experiments on ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.$

arXiv:cond-mat/0002257•Physical review. B, Condensed matter•Oct 1, 2000•4 citations

Low-energy theory of the t−t′−t″−U Hubbard model at half-filling: Interaction strengths in cuprate superconductors and an effective spin-only description of La2CuO4

Jean-Yves P. Delannoy, Michel J. P. Gingras, P. C. W. Holdsworth +1 more

Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on ${\text{La}}_{2}{\text{CuO}}_{4}$. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of $U$, $t$, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for ${\text{La}}_{2}{\text{CuO}}_{4}$. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.

arXiv:0808.3167•Physical Review B•Jun 24, 2009•57 citations

Effects of Double Magnon Scattering on the Particle-Particle Interaction in the Two-Dimensional Hubbard Model with Next-Nearest-Neighbor Hopping

Katsufumi Hashimoto

We investigate effects of double scattering by antiferromagnetic spin fluctuation (magnon), denoted as DMS, on both the singlet and triplet particle-particle (p-p) interaction in the two-dimensional Hubbard model. Different band structures with different next-nearest-neighbor hopping parameter but with a fixed electron occupation number of around 0.85 are considered. It is first indicated that due to the retardation of magnon contribution from the p-p and hole-hole (h-h) pair in the intermediate states also arises in the vertex correction, which has sign opposite to that of the usual particle-hole (p-h) pair. The contributions of the p-h pair and of the p-p and h-h pair to the DMS correction are enhanced for large and small momentum transfer (MT), respectively. A model calculation is performed to show that when the Fermi level is near the Van Hove level, the DMS correction becomes comparable to the single magnon results. For singlet pairing state the DMS p-p interaction is repulsive at both large and small MT, while for triplet pairing state it is attractive at both MT. This indicates that the odd frequency anisotropic s wave triplet state is a possible candidate for superconducting states of the model, in addition to the x 2 - y 2 wave singlet one.

Journal of the Physical Society of Japan•Jul 15, 2000•4 citations
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\ensuremath{-}J\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​.
Spectral properties of spin-wave excitations in the Mott-Hubbard antiferromagnet are studied in the intermediate-coupling regime, wherein extended-range spin couplings are present in the equivalent spin-1/2 Heisenberg model. A systematic expansion in powers of t2{\mathit{t}}^{2}t2/U2{\mathit{U}}^{2}U2 is developed for the spin-wave propagator in the random-phase approximation, and its quantitative usefulness is investigated. In two dimensions the spin-wave density of states exhibits a peak structure, resembling the broadening effect of spin-wave damping. Implications for recent light-pair scattering experiments in La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​ wherein the complete spin-wave spectrum is accessible in principle, are discussed.
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.
The Raman scattering spectra from magnetic excitations in an antiferromagnetic spin-12\frac{1}{2}21​ two leg ladder is investigated for weak and strong interladder coupling. In the first case, a cusp in the Raman intensity is obtained at a frequency twice the gap. In the second case, a peak at twice the gap replaces the cusp. We discuss the relevance of our calculation to recent experiments on CaV2O5{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}CaV2​O5​ and Sr14Cu24O41.{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.Sr14​Cu24​O41​.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of UUU, ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.
We investigate effects of double scattering by antiferromagnetic spin fluctuation (magnon), denoted as DMS, on both the singlet and triplet particle-particle (p-p) interaction in the two-dimensional Hubbard model. Different band structures with different next-nearest-neighbor hopping parameter but with a fixed electron occupation number of around 0.85 are considered. It is first indicated that due to the retardation of magnon contribution from the p-p and hole-hole (h-h) pair in the intermediate states also arises in the vertex correction, which has sign opposite to that of the usual particle-hole (p-h) pair. The contributions of the p-h pair and of the p-p and h-h pair to the DMS correction are enhanced for large and small momentum transfer (MT), respectively. A model calculation is performed to show that when the Fermi level is near the Van Hove level, the DMS correction becomes comparable to the single magnon results. For singlet pairing state the DMS p-p interaction is repulsive at both large and small MT, while for triplet pairing state it is attractive at both MT. This indicates that the odd frequency anisotropic s wave triplet state is a possible candidate for superconducting states of the model, in addition to the x 2 - y 2 wave singlet one.