Spin Dynamics of the One-Dimensional<i><i>J</i></i>-<i><i>J</i></i>' Model and Spin-Peierls Transition in CuGeO_<b>3</b>

Abstract

Spin dynamics as well as static properties of the one-dimensional J-J' model\n(S=1/2, J&gt;0 and 0\\le \\alpha=J'/J\\le 0.5) are studied by the exact\ndiagonalization and the recursion method of finite systems up to 26 sites.\nEspecially, the dynamical structure factor S(q,\\omega) is investigated\ncarefully for various values of \\alpha. As \\alpha increases beyond the\ngapless-gapful critical value \\alpha_c=0.2411, there appear features definitely\ndifferent from the Heisenberg model but the same with the Majumdar-Ghosh model.\nSome of these features depend only on the value of \\alpha and not on \\delta: a\nparameter introduced for the coupling alternation. By comparing these results\nwith a recent inelastic neutron scattering spectrum of an inorganic\nspin-Peierls compound CuGeO_3 [M. Arai et al.: Phys. Rev. Lett. 77 (1996)\n3649], it is found that the frustration by J' in CuGeO_3 is unexpectedly strong\n(\\alpha=0.4-0.45), and at least \\alpha must be larger than \\alpha_c to some\nextent. The value of J is evaluated at \\sim 180K consistent with other\nestimations. The coupling alternation is extremely small. This large\nfrustration is a primary origin of the various anomalous properties CuGeO_3\npossesses. For comparison we refer also to \\alpha'-NaV_2O_5.\n