Magnon-magnon interactions in the Spin-Peierls compound CuGeO₃

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In a magnetic substance the gap in the Raman spectrum, Deltaᵣ, is approximatively twice the value of the neutron scattering gap, Deltaₛ, if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO₃ the experimentally observed ratio Deltaᵣ/Deltaₛ is approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in the quasi-1D Spin-Peierls compound CuGe₃. We present numerical estimates for Deltaᵣ/Deltaₛ from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the Spin-Peierls phase. We discuss in detail the numerical method used, the dependence of the results on the model parameters and a novel matrix-element effect due to the dimerization of the Raman-operator in the Spin-Peierls phase.