The low-temperature thermal conductivity (kappa) of GdFeO_3 single crystals is found to be strongly dependent on magnetic field. The low-field kappa (H) curves show two dips for H parallel a and only one dip for H parallel c, with the characteristic fields having good correspondence with the spin-flop and the spin-polarization transitions. A remarkable phenomenon is that the subKelvin thermal conductivity shows hysteretic behaviors on the history of applying magnetic field, that is, the kappa(H) isotherms measured with field increasing are larger than those with field decreasing. Intriguingly, the broad region of magnetic field (sim 0--3 T) showing the irreversibility of heat transport coincides with that presenting the ferroelectricity. It is discussed that the irreversible kappa(H) behaviors are due to the phonon scattering by ferroelectric domain walls. This result shows an experimental feature that points to the capability of controlling the ferroelectric domain structures by magnetic field in multiferroic materials.
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