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Physical Review Letters

Magnetic Raman Scattering from 1D Antiferromagnets

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

Published Nov 4, 1996• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.77.4086

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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 ∣J2/J1∣\ensuremath≤0.3|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3∣J2​/J1​∣\ensuremath≤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.
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.
Motivated by various spin-1/2 compounds like Cs2CuCl4 or κ-(BEDT-TTF)2Cu2(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 J2/J1, the exchange constant ratio: ranging from J2 = 0, the well known square-lattice case, to J2/J1 = 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.
We consider Raman scattering of coupled two leg spin ladders in the Fleury-Loudon regime. We derive the dependence of the intensity with polarization of the incoming light and temperature and discuss the effect of interaction of the elementary excitations on the shape of the spectrum. We show that Raman scattering spectrum is sensitive to the effective dimensionality of the coupled ladder system, making Raman scattering useful to discriminate true ladder systems from quasi two dimensional spin gap systems.
Phase diagram of the antiferromagnetic J1J_1J1​-J2J_2J2​ spin-111 pyrochlore Heisenberg model
We study the phase diagram of the antiferromagnetic J1J_1J1​-J2J_2J2​ Heisenberg model on the pyrochlore lattice with S=1S=1S=1 spins at zero and finite temperatures. We use a combination of complementary state-of-the-art quantum many-body approaches such as density matrix renormalization group (DMRG), density-matrix purification and pseudo-Majorana functional renormalization group (PMFRG). We present an efficient approach to preserve the applicability of the PMFRG for spin-1 systems at finite temperatures despite the inevitable presence of unphysical spin states. The good performance of our methods is first demonstrated for the nearest-neighbor pyrochlore Heisenberg model where the finite temperature behavior of the specific heat and uniform susceptibility show excellent agreement within PMFRG and density-matrix purification. Including an antiferromagnetic second neighbor coupling we find that the non-magnetic ground-state phase of the nearest neighbor model extents up to $J_2/J_1 \sim 0.02 $ within DMRG, beyond which magnetic k=0\boldsymbol{k}=0k=0 long-range order sets in. Our PMFRG calculations find the phase transition in a similar regime J2/J1∼0.035(8)J_2/J_1\sim 0.035(8)J2​/J1​∼0.035(8) which, together with the DMRG result, provides a strong argument for the existence of a small but finite non-magnetic ground-state phase in the spin-1 pyrochlore Heisenberg model. We also discuss the origin of discrepancies between different versions of the functional renormalization group concerning the location of this phase transition.
We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one- and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator R\mathcal{R}R, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, R\mathcal{R}R contains terms beyond those appearing in the traditional Loudon-Fleury theory. Most saliently, a numerical implementation of the revised formalism to the case of the three-dimensional hyperhoneycomb Kitaev material $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ reveals that the non-Loudon-Fleury scattering terms actually dominate the Raman intensity. In addition, they induce a qualitative modification of the polarization dependence, including, e.g., the emergence of a sharp one-magnon peak at low energies, which is not expected in the traditional Loudon-Fleury theory. This peak is shown to arise from microscopic photon-assisted tunneling processes that are of similar type with the ones leading to the symmetric off-diagonal interaction $\mathrm{\ensuremath{\Gamma}}$ (known to be present in many Kitaev materials), but take the form of a bond-directional magnetic dipole term in the Raman vertex. These results are expected to apply across all Kitaev materials and mark a drastic change of paradigm for the understanding of Raman scattering in materials with strong spin-orbit coupling and multiple exchange paths.
We study the phase diagram of the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the pyrochlore lattice with S=1S=1S=1 spins at zero and finite temperatures. We use a combination of complementary state-of-the-art quantum many-body approaches such as density matrix renormalization group (DMRG), density-matrix purification, and pseudo-Majorana functional renormalization group (PMFRG). We present an efficient approach to preserve the applicability of the PMFRG for spin-1 systems at finite temperatures despite the inevitable presence of unphysical spin states. The good performance of our methods is first demonstrated for the nearest-neighbor pyrochlore Heisenberg model where the finite-temperature behavior of the specific heat and uniform susceptibility show excellent agreement within PMFRG and density-matrix purification. Including an antiferromagnetic second-neighbor coupling we find that the nonmagnetic ground-state phase of the nearest-neighbor model extents up to ${J}_{2}/{J}_{1}\ensuremath{\sim}0.02$ within DMRG, beyond which magnetic $\mathbit{k}=0$ long-range order sets in. Our PMFRG calculations find the phase transition in a similar regime ${J}_{2}/{J}_{1}\ensuremath{\sim}0.035(8)$ which, together with the DMRG result, provides a strong argument for the existence of a small but finite nonmagnetic ground-state phase in the spin-1 pyrochlore Heisenberg model. We also discuss the origin of discrepancies between different versions of the functional renormalization group concerning the location of this phase transition.