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Progress of Theoretical Physics Supplement

Calculation of Magnetic Raman Spectra by the Exchange-Scattering in Antiferromagnetic Ladder with Two-Legs

Toshihiko Suzuki, Shinichiro Tada, Yuichi Watabe, Yuhei Natsume

Published Jan 1, 2000• 2 citations
Publisher

Abstract

The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder with 12 × 2 sites. We adopt the continued-fraction to the calculation of the spectral function in the process of the Lanczos method. The result suggests that the characteristic structure appearing at 4 or 5 times the spin-gap. The calculation is compared with recent Raman spectra observed in Sr14−xCaxCu24O41.

DOI
10.1143/ptps.138.523

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The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder with 12 × 2 sites. We adopt the continued-fraction to the calculation of the spectral function in the process of the Lanczos method. The result suggests that the characteristic structure appearing at 4 or 5 times the spin-gap. The calculation is compared with recent Raman spectra observed in Sr14−xCaxCu24O41.
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.
Characteristic properties of excited states in anitiferromagnetic ladder systems with spin-1/2 are investigated in relation with the theoretical analysis of the quite asymmetric shape of the peak for twice the spin gap Δg in magnetic Raman spectra. Here, the structure of exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which legs with antiferromagnetic bond Jc is connected by rungs with antiferromagnetic bond Jr. The singlet ground state in this system can be expressed as the ordering of singlet dimers on rungs in the ladder for Jc/Jr →+0. In fact, the value of 0.1 is adopted to be the ratio of Jc /Jr in order to discuss the experimental work of the magnetic Raman spectra for the ladder of V4+ ions in the oxide compound CaV2O5 reported in Konstantinović et al., Phys. Rev. B61 (2000), 15185. As for this peak of 2Δg , quite an asymmetric observed shape is explained by the present calculation. According to the analysis of spectra, we discuss the expression of excited states by triplet dimers on rungs: The dominant contribution of the pair of triplet dimers on adjacent rungs to the corresponding state for 2Δg peak is pointed out.
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 Raman response in the antiferromagnetic 2-leg S = 1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV 2 O 5 and La y Ca 14 − y Cu 24 O 41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.
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.