Magnon-magnon interactions in the Spin-Peierls compound CuGeO_3

TL;DR

This paper investigates magnon-magnon interactions in CuGeO_3, revealing attractive interactions and a continuum of two-magnon bound states through numerical studies and analysis of Raman spectra.

Contribution

It provides numerical estimates of the Raman to neutron gap ratio and introduces a novel matrix-element effect related to dimerization in the Spin-Peierls phase.

Findings

Observed ratio Delta_R/Delta_S between 1.49 and 1.78 indicating attractive magnon interactions

Numerical estimates agree with experimental data for certain frustration parameters

Postulation of a continuum of two-magnon bound states in the Spin-Peierls phase

Abstract

In a magnetic substance the gap in the Raman spectrum, Delta_R, is approximatively twice the value of the neutron scattering gap, Delta_S, if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO_3 the experimentally observed ratio Delta_R/Delta_S is approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in the quasi-1D Spin-Peierls compound CuGe_3. We present numerical estimates for Delta_R/Delta_S 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.