Triplet Waves in a Quantum Spin Liquid

We report a neutron scattering study of the spin- $1/2$ alternating bond antiferromagnet $\mathrm{Cu}({\mathrm{NO}}_3{)}_2̇2.5{\mathrm{D}}_2\mathrm{O}$ for $0.06<\mathrm{}{k}_{B}T/J_1<1.5\mathrm{}$. For $k_{B}T/J_1\ll 1$ the excitation spectrum is dominated by a coherent singlet-triplet mode centered at $J_1=0.442\mathrm{}\left(2\right)\mathrm{meV}$ with sinusoidal dispersion and a bandwidth of $J_2=0.106\mathrm{}\left(2\right)\mathrm{meV}$. A complete description of the zero temperature contribution to the scattering function from this mode is provided by the single mode approximation. At finite temperatures we observe exponentially activated band narrowing and damping. The relaxation rate is thermally activated and wave vector dependent with the periodicity of the reciprocal lattice.