Thermodynamics and ground states of spin ice on a bulk hexagonal lattice

The paper considers the magnetic structure of Ising-like point dipoles located on the edges of a three-dimensional hexagonal lattice with vectors of magnetic moments oriented along the edges of the lattice. The volume lattice of spin ice is a multilayer stacked flat hexagonal lattice without shifting the layers relative to each other. Between the layers are added dipoles with magnetic moment directed perpendicularly to the layer. Such interlayer dipoles correlate the configurations in the lattice nodes and influence the magnetic ordering of the spin ice structure. The critical distance between layers at which all pairwise energies of spins adjacent to the lattice node are compensated is analytically obtained. For three cases when the distance is less than critical, equal and greater than critical, the configurations of ground states are described. The temperature behaviors of the mean energy and heat capacity are obtained by the Metropolis method for all three cases. In all cases in the system there are two temperature phases “order” and “orderless”, while for two-dimensional spin ice on a hexagonal lattice the order phase is divided into “far” and “close”. For the case when the interlayer distance is below the critical distance, the ground state is not degenerate, the system is dominated by the near order. For the case when the interlayer distance is above the critical distance, the multiplicity of degeneracy of the ground state depends on the number of spins, the ordering of the system is also given by the nearest dipole-dipole interactions. When the interlayer distance is equal to the critical distance, the ground state is degenerate 6 times, the near interactions are fully compensated, and the long-range order dominates.