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arXiv:cond-mat/9505012 · Physical Review Letters

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

Franco Nori, Roberto D. Merlin, Stephan Haas, Anders W. Sandvik, Elbio R. Dagotto

Published Jul 17, 1995• 42 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.75.553

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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.
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 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.
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.
Quantum magnets in two dimensions display strong quantum interaction effects even when magnetically ordered. Using the metal-organic framework material CuF2_22​(D2_22​O)2_22​(pyz), we investigate the field-dependent spin dynamics of the S=1/2S = 1/2S=1/2 square-lattice Heisenberg antiferromagnet by high-resolution inelastic neutron scattering to applied fields beyond one third of saturation. We discover an anomalously sharp, dispersive ``shadow mode'' residing within the two-magnon continuum, which shadows the dispersion of the transverse one-magnon branches across the Brillouin zone at an offset equal to the Larmor energy. We perform cylinder matrix-product-state (MPS) calculations that reproduce the field-induced spectrum quantitatively and apply a spectrally consistent 1/S1/S1/S spin-wave theory to deduce that the ``Larmor-shadow mode'' is a composite two-magnon resonance: a dispersing magnon at wavevector Q{\bf Q}Q couples to the uniform Larmor precession at ΓΓΓ, its small intrinsic linewidth indicating a non-perturbative effect of attractive magnon-magnon interactions. Another quantum-fluctuation phenomenon, the zero-field (π,0)(π,0)(π,0) anomaly, is lost at increasing fields, which tighten the spectral weight into the one-magnon and Larmor-shadow modes. To our knowledge, these results constitute the first observation of a sharp quasi-bound state embedded in the continuum of a gapless two-dimensional antiferromagnet.
Abstract Quantum magnets in two dimensions display strong quantum interaction effects even when magnetically ordered. Using the metal-organic framework material CuF 2 (D 2 O) 2 (pyz), we investigate the field-dependent spin dynamics of the S = 1/2 square-lattice Heisenberg antiferromagnet by high-resolution inelastic neutron scattering to applied fields beyond one third of saturation. We discover an anomalously sharp, dispersive “shadow mode” residing within the two-magnon continuum, which shadows the dispersion of the transverse one-magnon branches across the Brillouin zone at an offset equal to the Larmor energy. We perform cylinder matrix-product-state (MPS) calculations that reproduce the field-induced spectrum quantitatively and apply a spectrally consistent 1/ S spin-wave theory to deduce that the “Larmor-shadow mode” is a composite two-magnon resonance: a dispersing magnon at wavevector Q couples to the uniform Larmor precession at Γ, its small intrinsic linewidth indicating a non-perturbative effect of attractive magnon-magnon interactions. Another quantum-fluctuation phenomenon, the zero-field (π, 0) anomaly, is lost at increasing fields, which tighten the spectral weight into the one-magnon and Larmor-shadow modes. To our knowledge, these results constitute the first observation of a sharp quasi-bound state embedded in the continuum of a gapless two-dimensional antiferromagnet.
Motivated by various spin-1/2 compounds like Cs 2 CuCl 4 or κ - (BEDT - TTF) 2 Cu 2 (CN) 3 , we derive a Raman-scattering operator à la Shastry and Shraiman for various geometries. For T = 0, the exact spectra are computed by the Lanczos algorithm for finite-size clusters. We perform a systematic investigation as a function of J 2 / J 1 , the exchange constant ratio: ranging from J 2 = 0, the well known square-lattice case, to J 2 / J 1 = 1 the isotropic triangular lattice. We discuss the polarization dependence of the spectra and show how it can be used to detect precursors of the instabilities of the ground state against quantum fluctuations.