Spin Dynamics of the One-Dimensional J-J′ Model and Spin-Peierls Transition in CuGeO₃

Spin dynamics as well as static properties of the one-dimensional J-J′ model (5 = 1/2, J > 0 and 0 ≤ α = Jα/J ≤ 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, w) is investigated carefully for various values of α. As α increases 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 α and 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 CuGeO₃ [M. Arai et al.: Phys. Rev. Lett. 77 (1996) 3649], it is found that the frustration by J′ in CuGeO₃ is unexpectedly strong (α = 0.4-0.45). and at least a must be larger than α_c to some extent. The value of J is evaluated at ∼ 180 K consistent with other estimations. The coupling alternation is extremely small. This large frustration is a primary origin of the various anomalous properties CuGeO₃ possesses. For comparison we refer also to α′-NaV₂O₅.