  Dy$_2$Ti$_2$O$_7$ is at present the cleanest example of a spin-ice material.
Previous theoretical and experimental work on the first-order transition
between the kagome-ice and the fully polarized state has been taken as a
validation for the dipolar spin-ice model. Here we investigate in further depth
this phase transition using ac-susceptibility and dc-magnetization, and compare
this results with Monte-Carlo simulations and previous magnetization and
specific heat measurements. We find signatures of an intermediate state between
the kagome-ice and full polarization. This signatures are absent in current
theoretical models used to describe spin-ice materials.
