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We have used a combination of neutron resonant spin-echo and triple-axisspectroscopies to determine the energy and linewidth of the magnon resonance inIPA-Cu(Cl$_{0.95}$Br$_{0.05}$)$_3$, a model spin-1/2 ladder antiferromagnetwhere Br substitution induces bond randomness. We find that the bond defectsinduce a blueshift, $\delta \Delta$, and broadening, $\delta \Gamma$, of themagnon gap excitation compared to the pure compound. At temperatures exceedingthe energy scale of the inter-ladder exchange interactions, $\delta \Delta$ and$\delta \Gamma$ are temperature independent within the experimental error, inagreement with Matthiessen's rule according to which magnon-defect scatteringyields a temperature independent contribution to the magnon mean free path.Upon cooling, $\delta \Delta$ and $\delta \Gamma$ become temperature dependentand saturate at values lower than those observed at higher temperature,consistent with the crossover from one-dimensional to two-dimensional spincorrelations with decreasing temperature previously observed in pureIPA-CuCl$_3$. These results indicate limitations in the applicability ofMatthiessen's rule for magnon scattering in low-dimensional magnets.

Bond Randomness Induced Magnon Decoherence in a Spin-1/2 Ladder Compound