Study of the magnetic susceptibility in the spin-Peierls system CuGeO$_3$

Abstract

We study numerically, using a one-dimensional Heisenberg model, the spin-Peierls transition in the linear Cu$^{2+}$ spin-1/2 chains in the inorganic compound 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 $160\:\rm K$, and that the next nearest neighbor exchange parameter is approximately $0.36\:\rm J$.