Ground state candidate and thermodynamics of Apamea spin ice

We consider the dipolar spin ice on a 2D Apamea lattice whose geometry is derived from the square spin ice. We propose ground-state candidate configurations and show that not all vertices are in energetically favorable states. There is no macroscopic degeneracy of the ground-state candidate. By using the numerical Metropolis method, we demonstrate the existence of three phases of magnetic order and explain their origins. A good agreement between the Metropolis and XMCD experiment is demonstrated, and the improved Apamea lattice geometry for the experimental observation of the dynamics in the ordered state is proposed.