Spin Dynamics of the One-Dimensional J-J' Model and Spin-Peierls Transition in CuGeO_3

Abstract

Spin dynamics as well as static properties of the one-dimensional J-J' model (S=1/2, J>0 and 0\le α=J'/J\le 0.5) are studied by the exact diagonalization and the recursion method of finite systems up to 26 sites. Especially, the dynamical structure factor S(q,ω) is investigated carefully for various values of α. As αincreases beyond the gapless-gapful critical value α_c=0.2411, there appear features definitely different from the Heisenberg model but the same with the Majumdar-Ghosh model. Some of these features depend only on the value of αand not on δ: a parameter introduced for the coupling alternation. By comparing these results with a recent inelastic neutron scattering spectrum of an inorganic spin-Peierls compound CuGeO_3 [M. Arai et al.: Phys. Rev. Lett. 77 (1996) 3649], it is found that the frustration by J' in CuGeO_3 is unexpectedly strong (α=0.4-0.45), and at least αmust be larger than α_c to some extent. The value of J is evaluated at \sim 180K consistent with other estimations. The coupling alternation is extremely small. This large frustration is a primary origin of the various anomalous properties CuGeO_3 possesses. For comparison we refer also to α'-NaV_2O_5.