  Low-temperature thermal conductivity (\kappa), as well as magnetization (M)
and electric polarization (P), of multiferroic orthoferrite DyFeO_3 single
crystals are studied with H \parallel c. When the crystal is cooled in zero
field, M, P, and \kappa all consistently exhibit irreversible magnetic-field
dependencies. In particular, with 500 mK < T \le 2 K, all these properties show
two transitions at the first run of increasing field but only the higher-field
transition is present in the subsequent field sweepings. Moreover, the
ultra-low-T (T < 500 mK) \kappa(H) shows a different irreversibility and there
is only one transition when the field is swept both up and down. All the
results indicate a complex low-T H-T phase diagram involving successive
magnetic phase transitions of the Fe^{3+} spins. In particular, the ground
state, obtained with cooling to subKelvin temperatures in zero field, is found
to be an unexplored phase.
