Bond randomness induced magnon decoherence in a spin-$\frac{1}{2}$ 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 blue shift, $\delta \Delta$, and broadening, $\delta \Gamma$, of the magnon gap excitation compared to the pure compound. At temperatures exceeding the energy scale of the interladder exchange interactions, $\delta \Delta$ and $\delta \Gamma$ 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, $\delta \Delta$ and $\delta \Gamma$ 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.

Figure 1

Typical constant-$q$ scans measured on a cold-TAS spectrometer in IPA-Cu(Cl${}_{0.95}$Br${}_{0.05}$)${}_3$ at $q=(1.5,0,0)$ at different temperatures. The solid lines are the results of fits to Lorentzians convoluted with the resolution function of the instrument. Scans at different temperatures are shifted vertically for clarity.

Figure 2

(a) Temperature dependence of the magnon energy gap $\Delta$ for IPA-Cu(Cl${}_{0.95}$Br${}_{0.05}$)${}_3$ (red rectangles). Blue points are for IPA-CuCl${}_3$ from Refs. 5 and 7. Empty and filled symbols represent data collected by NRSE and TAS techniques, respectively. The blue line is the result of a calculation based on a NL$\sigma$M with ${\Delta }_0=1.44$ meV and interladder interaction $J_{\perp }/J=0.1$, following Ref. 24. The red line is shifted by $0.25$ meV relative to the blue one. (b) Temperature dependence of the bond randomness induced magnon blue shift of the 5$\%$ Br substituted compound. The broad shaded line is a guide to the eyes.

Figure 3

(a) Temperature dependence of the magnon linewidth $\Gamma$. Blue points are from Refs. 5 and 7. Red rectangles are the result of the present study. Empty and filled symbols represent data collected by NRSE and TAS techniques, respectively. The line represents NL$\sigma$M calculations[25] with ${\Delta }_0=1.44$ meV. (b) Temperature dependence of the magnon decoherence induced by bond randomness of the 5$\%$ Br substituted compound. The broad shaded guide to the eyes line used here is the same as in Fig. 2 but divided by a factor 2.