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arXiv:cond-mat/0002257 · Physical review. B, Condensed matter

Raman scattering cross section of spin ladders

E. Orignac, R. Citro

Published Oct 1, 2000• 4 citations
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Abstract

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 ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.$

DOI
10.1103/physrevb.62.8622

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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​.
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.
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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.
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.
A model of coupled antiferromagnetic spin-1/2 Heisenberg ladders is studied with numerical techniques. In the case of ferromagnetic interladder coupling we find that the dynamic and static structure factor has a peak at $(\ensuremath{\pi},\ensuremath{\pi}/2)$ where the first (second) direction is along (transversal) to the ladders. In addition, we suggest that the intensity of this peak and the spin-spin correlation at the maximum distance along the ladder direction remain finite in the bulk limit for strong enough interladder coupling. We discuss the relevance of these results for magnetic compounds containing ladders coupled in a trellis lattice and for the stripe scenario in high-Tc{T}_{c}Tc​ superconducting cuprates.