  We report a study of the low-temperature thermal conductivity (\kappa) of
pure and Zn-doped LiCu_2O_2 single crystals. The \kappa(T) of pure LiCu_2O_2
single crystal shows a double-peak behavior, with two peaks locating at 48 K
and 14 K, respectively. The different dependences of the peaks on the Zn
concentration indicate that the high-T peak is likely due to the phonon
transport while the low-T one is attributed to the magnon transport in the spin
spiral ordering state. In addition, the magnetic field can gradually suppress
the low-T peak but does not affect the high-T one; this further confirms that
the low-T peak is originated from the magnon heat transport.
