We report the first measurement of magnon thermal conductivity in monodomain single crystals of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the U2D2 antiferromagnetic phase. The magnon mean free path λ was found first to rise rapidly upon cooling below ${\mathit{T}}_{\mathit{N}}$ and then more slowly at low temperatures, depending on the sample. The temperature dependence is consistent with magnon umklapp scattering at high T, i.e., λ proportional to ${\mathit{T}}^{\mathrm{-}2}$ exp(Δ/${\mathit{k}}_{\mathit{B}}$T), with Δ/${\mathit{k}}_{\mathit{B}}$ determined to be 5.8(±0.3) mK. The limiting low-temperature values of λ varied from 0.3 to 3 μm.

• Received 15 August 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.1450