Rapid Suppression of the Spin Gap in Zn-doped CuGeO$_3$ and SrCu$_2$O$_3$

The influence of non-magnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO$_3$ is studied. A simple extension to Zn-doped ${\rm Sr Cu_2 O_3}$ is also discussed. Using Exact Diagonalization techniques and intuitive arguments we show that Zn-doping introduces states in the Spin-Peierls gap of CuGeO$_3$. This effect can be understood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Similar arguments apply to ladders with non-magnetic impurities simply replacing the tendency to dimerization in CuGeO$_3$ by the tendency to form spin-singlets along the rungs in SrCu$_2$O$_3$.