Two-magnon Raman scattering in spin-ladder geometries and the ratio of rung and leg exchange constants

We discuss ways in which the ratio of exchange constants along the rungs and legs of a spin-ladder material influences the two-magnon Raman scattering spectra and hence can be determined from it. We show that within the Fleury-Loudon-Elliott approach, the Raman line shape does not change with polarization geometries. This line shape is well known to be difficult to calculate accurately from theory. However, the Raman scattering intensities do vary with polarization geometries, which are easy to calculate. With some assumptions about the Raman scattering Hamiltonian, the latter can be used to estimate the ratio of exchange constants. We apply these results to the recent measurements of Sugai et al. of Raman scattering from spin-ladder materials such as ${\mathrm{La}}_{6}{\mathrm{Ca}}_{8}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.$