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arXiv:cond-mat/0012069

Raman Scattering from Magnetic Excitations in coupled Spin Ladders

R. Citro, E. Orignac

Published Dec 6, 2000• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0012069

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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.
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​.
Recent experiments have revealed the role of the staggered Dzyaloshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin-1∕21∕21∕2 two-leg ladder compound under a uniform magnetic field. We derive a low-energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzyaloshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzyaloshinskii-Moriya interaction using exact diagonalizations.
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.
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.
The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.
Motivated by the lack of an obvious spectroscopic probe to investigate nonconventional order such as quadrupolar orders in spin S>12S>\frac{1}{2}S>21​ systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S=12S=\frac{1}{2}S=21​ case, where the only type of local excited state is a doubly occupied state of energy UUU, several local excited states with occupation up to four electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}U$, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-12\frac{1}{2}21​ case. For $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}4U$, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling $\ensuremath{\sim}{({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{j})}^{2}$. Consequences for the Raman spectra of S=1S=1S=1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.