CALCULATION OF LIGHT SCATTERING SPECTRA RELATED TO LOW-ENERGY EXCITATION IN LOW-DIMENSIONAL QUANTUM ANTIFERROMAGENTICS SYSTEMS

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The low-dimensional antiferromagnetic systems have quite characteristic features. In fact, much work for ground states has been made up to now. On the other hand, optical properties of low-lying excited states on spin-gaps in these systems have been reported by relatively small number of papers. In particular, the magnetic Raman-scattering has been discussed by only a few papers. In the present investigation, we reproduce spectra for the exchange-scattering mechanism in two-leg ladder quantum antiferromagnetic systems by the numerical calculation. We treat the finite Heisenberg ladders, in which legs with antiferromagnetic bonds J_c are connected by rungs with antiferromagnetic, bonds J_r. The calculation is made in the system of 50 x 2 sites with spin=1/2 by the perturbation method for the extension of J_c/J_r, in addition to that in 12 x 2 by the exact diagonalization. The singlet ground states are expressed as the oderings of singlet dimers on rungs for small value of J_c/J_r, while excited states can be described as the patterns for triplet dimers on rungs. In fact, we can make clear the origin of the characteristic shapes of magneitc Raman spectra observe at twice the spin-gaps in C_aV_2O_5. Namely, this asymmetric shape is explained by the fact that the corresponding excited states with large transition moments are composed of patterns of pairs for triplet dimers on adjacent rings. The agreement between the present calculation and the observed spectra is quite well. Furthermore, we investigate magnetic Raman spectra in two-leg ladder systems Sr_<14-x>Ca_xCu_<24>O_<41> with relatively large values of J_c/J_r. By the present analyzes of magnetic Raman spectra in low-dimensional quantum antiferromagnetic systems, we can propose the powerful method for understanding properties of excited states and the origin of spin-gaps.