Anisotropic release of the residual zero-point entropy in the spin ice compound ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7:$ Kagome ice behavior

We report the specific heat and entropy of single crystals of the spin ice compound ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions [100], [110], [111], and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches $R\ln 2.$ However, in the intermediate-field region, the entropy in the fields along the [111] direction is different from those for the other three field directions. For the [111] direction, the frustration structure changes from that of the three-dimensional pyrochlore to that of a two-dimensional Kagome-like lattice with constraint due to the ice rule, leading to different values of the zero-point entropy.