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The low-temperature thermal conductivity (\kappa) of GdFeO_3 single crystalsis 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-flopand the spin-polarization transitions. A remarkable phenomenon is that thesubKelvin thermal conductivity shows hysteretic behaviors on the history ofapplying magnetic field, that is, the \kappa(H) isotherms measured with fieldincreasing are larger than those with field decreasing. Intriguingly, the broadregion of magnetic field (\sim 0--3 T) showing the irreversibility of heattransport coincides with that presenting the ferroelectricity. It is discussedthat the irreversible \kappa(H) behaviors are due to the phonon scattering byferroelectric domain walls. This result shows an experimental feature thatpoints to the capability of controlling the ferroelectric domain structures bymagnetic field in multiferroic materials.

Magnetic phase transitions and magnetoelectric coupling of GdFeO_3 single crystals probed by low-temperature heat transport