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

We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy and linewidth of the magnon resonance in IPA-Cu(Cl$_{0.95}$Br$_{0.05}$)$_3$, a model spin-1/2 ladder antiferromagnet where Br substitution induces bond randomness. We find that the bond defects induce a blueshift, $δΔ$, and broadening, $δΓ$, of the magnon gap excitation compared to the pure compound. At temperatures exceeding the energy scale of the inter-ladder exchange interactions, $δΔ$ and $δΓ$ are temperature independent within the experimental error, in agreement with Matthiessen's rule according to which magnon-defect scattering yields a temperature independent contribution to the magnon mean free path. Upon cooling, $δΔ$ and $δΓ$ become temperature dependent and saturate at values lower than those observed at higher temperature, consistent with the crossover from one-dimensional to two-dimensional spin correlations with decreasing temperature previously observed in pure IPA-CuCl$_3$. These results indicate limitations in the applicability of Matthiessen's rule for magnon scattering in low-dimensional magnets.