The heat transport phenomenon in the two-dimensional Heisenberg ferromagnet K
2CuF
4 in investigated through the measurement of thermal conductivity under the magnetic field. The evidence and the quantitative estimation to magnon conductivity are obtained below the ordering temperature
Tc. In the vicinity of
Tc the anomalous dip of the conductivity, representing the phonon scattering by the critical fluctuation of spins, is observed. Above
Tc, the enhanced conduction is also found, which is attributed to the diffusion or paramagnetic magnon.
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