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We study the low-temperature thermal conductivity (\kappa) of Dy_2Ti_2O_7 andYb_2Ti_2O_7 single crystals in magnetic fields up to 14 T along the [111],[100] and [110] directions. The main experimental findings for Dy_2Ti_2O_7 are:(i) the low-T \kappa(H) isotherms exhibit not only the step-like decreases atthe low-field (< 2 T) magnetic transitions but also obvious field dependenciesin high fields (> 7 T); (ii) at T \le 0.5 K, the \kappa(H) curves showanisotropic irreversibility in low fields, that is, the \kappa(H) hysteresislocates at the first-order transition with H \parallel [100] and [110], whileit locates between two successive transitions with H \parallel [111]; (iii) the\kappa in the hysteresis loops for H \parallel [100] and [110] show anextremely slow relaxation with the time constant of \sim 1000 min. The mainexperimental findings for Yb_2Ti_2O_7 are: (i) the zero-field \kappa(T) show akink-like decrease at the first-order transition (\sim 200 mK) with decreasingtemperature; (ii) the low-T \kappa(H) isotherms show a decrease in low fieldand a large enhancement in high fields; (iii) the low-T \kappa(H) curves show asharp minimum at 0.5 T for H \parallel [110] and [111]. The roles of monopoleexcitations, field-induced transitions, spin fluctuations and magnetoelasticcoupling are discussed.

Low-temperature thermal conductivity of Dy_2Ti_2O_7 and Yb_2Ti_2O_7 single crystals