We study numerically, using a one-dimensional Heisenberg model coupled to the lattice in the adiabatic approximation, the spin-Peierls transition in the linear ${\mathrm{Cu}}^{2+}$ spin-1/2 chains in the inorganic compound ${\mathrm{CuGeO}}_3$, which has been recently observed experimentally. We suggest that the magnetic susceptibility, the temperature dependence of the spin gap, and the spin-Peierls transition temperature of this material can be reasonably described by including nearest and next-nearest-neighbor antiferromagnetic interactions along the chain. We estimate that the nearest-neighbor exchange parameter J is approximately 160 K, and that the next-nearest-neighbor exchange parameter is approximately 0.36J.

• Received 28 February 1995

DOI:https://doi.org/10.1103/PhysRevB.51.16098