Ordered Phase of the Dipolar Spin Ice under [110]-Magnetic Fields
We find that the true ground state of the dipolar spin ice system under [110]-magnetic fields is the ``Q=X'' structure, which is consistent with both experiments and Monte Carlo simulations. We then perform a Monte Carlo simulation to confirm that there exists a first order phase transition under the [110]-field. In particular this result indicates the existence of the first order phase transition to the ``Q=X'' phase in the field above 0.35 T for Dy2Ti2O7. We also show the magnetic field-temperature phase diagram to summarize the ordered states of this system.