Magnetic anisotropy of the spin-ice compound ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

We report magnetization and ac susceptibility of single crystals of the spin-ice compound ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7.$ Saturated moments at 1.8 K along the characteristic axes [100] and [110] agree with the expected values for an effective ferromagnetic nearest-neighbor Ising pyrochlore with local $〈111〉$ anisotropy, where each magnetic moment is constrained to obey the “ice rule.” At high enough magnetic fields along the [111] axis, the saturated moment exhibits a breaking of the ice rule; it agrees with the value expected for a three-in, one-out spin configuration. Assuming the realistic magnetic interaction between Dy ions given by the dipolar spin ice model, we completely reproduce the results at 2 K by Monte Carlo calculations. However, down to at least 60 mK, we have not found any experimental evidence of the long-range magnetic ordering predicted by this model to occur at around 180 mK. Instead, we confirm the spin freezing of the system below 0.5 K.