The J_1-J_2 model revisited : Phenomenology of CuGeO_3

Abstract

We present a mean field solution of the antiferromagnetic Heisenberg chain with nearest (J_1) and next to nearest neighbor (J_2) interactions. This solution provides a way to estimate the effects of frustration. We calculate the temperature-dependent spin-wave velocity, v_s(T) and discuss the possibility to determine the magnitude of frustration J_2/J_1 present in quasi 1D compounds from measurements of v_s(T). We compute the thermodynamic susceptibility at finite temperatures and compare it with the observed susceptibility of the spin-Peierls compound CuGeO_3. We also use the method to study the two-magnon Raman continuum observed in CuGeO_3 above the spin-Peierls transition.Comment: Phys. Rev.