Analytic model for low energy excitation states and phase transitions in spin-ice systems.

Low energy excitation states in magnetic structures of the so-called spin-ices are produced via spin flips among contiguous tetrahedra of their crystal structure. These spin flips generate entities which mimic magnetic dipoles in every two tetrahedra according to the dumbbell model. When the temperature increases, the spin-flip processes are transmitted in the lattice, generating so-called Dirac strings, which constitute structural entities that can present mimetic behavior similar to that of magnetic monopoles. In recent studies of both specific heat and ac magnetic susceptibility, two (even possibly three) phases have been shown to vary the temperature. The first of these phases presents a sharp peak in the specific heat and another phase transition occurs for increasing temperature whose peak is broader than that of the former phase. The sharp peak occurs when there are no free individual magnetic charges and temperature of the second phase transition coincides with the maximum proliferation of free deconfined magnetic charges. In the present paper, we propose a model for analyzing the low energy excitation many-body states of these spin-ice systems. We give analytical formulas for the internal energy, specific heat, entropy and their temperature evolution. We study the description of the possible global states via the nature and structure of their one-body components by means of the thermodynamic functions. Below 0.37 K, the Coulomb-like magnetic charge interaction can generate a phase transition to a condensation of pole-antipole pairs, possibly having Bose-Einstein structure which is responsible for the sharp peak of the first phase transition. When there are sufficient free positive and negative charges, the system tends to behave as a magnetic plasma, which implies the broader peak in the specific heat appearing at higher temperature than the sharper experimental peak.