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arXiv:cond-mat/0411700 · Physical Review B

Two-magnon Raman scattering in spin ladders with exact singlet-rung ground state

P. N. Bibikov

Published Jul 22, 2005• 6 citations
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Abstract

Using coordinate Bethe ansatze we construct two-magnon states for the family of spin-ladder models with exact singlet-rung vacuum suggested by A. K. Kolezhuk and H.-J. Mikeska. The explicit formula for the zero-temperature Raman scattering cross section is derived. The corresponding line shapes are strongly asymmetric and their singularities originate only from bound states. This form of a line shape is in good correspondence to the experimental data.

DOI
10.1103/physrevb.72.012416

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Using coordinate Bethe ansatze we construct two-magnon states for the family of spin-ladder models with exact singlet-rung vacuum suggested by A. K. Kolezhuk and H.-J. Mikeska. The explicit formula for the zero-temperature Raman scattering cross section is derived. The corresponding line shapes are strongly asymmetric and their singularities originate only from bound states. This form of a line shape is in good correspondence to the experimental data.
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One-magnon problem for spin-ladders with exact singlet-rung ground state in arbitrary oriented constant and staggered magnetic fields is studied. For two special configurations when the both fields are parallel or perpendicular to each other the exact formulas for eigenstates and eigenvectors are presented. In the parallel case the one-magnon contribution to the ESR absorption line shape is obtained. The latter is non-Lorentzian, has finite range and a gap around resonance. For low fields both the range of the spectrum and the width of the gap are controlled by the width of the one-magnon zone in zero magnetic field. Some other interactions usually contributing to the ESR line shape are also briefly discussed.
Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for mmm-magnon (m>3m>3m>3) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.
We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
We present a family of spin-ladder models which can be solved exactly for the ground state and exhibit non-Haldane spin-liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. 78, 3939 (1997)], and study their excitation spectra using a simple variational Ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
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.