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

Abstract

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.

Two fluid model in low energy excited states within spin-ice systems

“…In the ground state the number of confined dipoles in each pair of two contiguous tetrahedrons must be zero and therefore the specific heat at zero kelvins should be null, as it appears in our results as well as in other investigations 25,42,46 . On the contrary, in other experimental results 27,47 and other obtained by statistical procedures as in refs 26,44 this logic characteristic is not reflected in their results.…”

“…The conditions in both cases are different but compatible. In addition, in the latter case, a wave function that is inspired by the BCS theory is proposed 46 . By further increasing temperatures, the confined dipoles break progressively and then the free magnetic charges evaporate from BS or BEC and form a Coulomb gas of free charges of different signs whose structure is that of a cold magnetic plasma.…”

A Model of Two Quantum Fluids for the Low Energy Excited States of the Systems with Entities That Mimic the Magnetic Monopoles

“…When spin flips produce the existence of magnetic dipoles, conceived as established by the dumbbell model, the term of interaction of Equation ( 1) favors the existence of a bosonic condensation, such as has been published in other research [47,48]. Such condensation can be analyzed by the thermodynamic potential that defines a global state, whose components, |p i a i = √ 2 2 (|0, 0 i + |1, 0 i ), are a quantum composition of spin 0 and spin 1 bosonic states.…”

“…In a first step, we do consider the energy of a dipole state when a vertex between two contiguous tetrahedra is produced by a spin flip; therefore, we have two magnetic charges, one in each of these two tetrahedra. This energy was calculated in reference [47,48].…”

“…is the first order perturbation energy due to the negative interaction of magnetic charges of different signs [47,48].…”