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

Abstract

Spin dynamics as well as static properties of the one-dimensionalJ-J' model (S=1/2, J>0 and 0≤ α=J'/J≤ 0.5) arestudied by the exact diagonalization and the recursion methodof finite systems up to 26 sites.Especially, the dynamical structure factor S(q, ω) isinvestigated carefully for various values of α.As α increases beyond the gapless-gapful critical valueα_c=0.2411, there appear features definitely differentfrom the Heisenberg model but the same with the Majumdar-Ghosh model.Some of these features depend only on the value of α andnot on δ: a parameter introduced for the coupling alternation.By comparing these results with a recent inelastic neutron scatteringspectrum of an inorganic spin-Peierls compound CuGeO₃[M. Arai et al.: Phys. Rev. Lett. 77 (1996) 3649], it is found thatthe frustration by J' in CuGeO₃ is unexpectedly strong(α=0.4--0.45), and at least α must be larger thanα_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 anomalousproperties CuGeO₃ possesses.For comparison we refer also to α'-NaV₂O₅.