To study the effects of paramagnetic spins on phonons, both the in-plane and the c-axis heat transport of GdBaCo_{2}O_{5+x} (GBCO) single crystals are measured at low temperature down to 0.36 K and in magnetic field up to 16 T. It is found that the phonon heat transport is very strongly affected by the magnetic field and nearly 5 times increase of the thermal conductivity in several Tesla field is observed at 0.36 K. It appears that phonons are resonantly scattered by paramagnetic spins in zero field and the application of magnetic field removes such strong scattering, but the detailed mechanism is to be elucidated.
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