Thermodynamics of elementary excitations in artificial magnetic square ice

TL;DR

This study explores how temperature affects elementary excitations like magnetic monopoles in artificial square spin ice systems, revealing phase transition signatures and size-dependent monopole separation behaviors.

Contribution

It provides the first detailed thermodynamic analysis of monopole excitations in artificial square ice considering only dipolar interactions, highlighting size effects and phase transition indicators.

Findings

Specific heat exhibits a sharp peak at T_p.

Average monopole separation peaks at T_p.

Monopole separation increases logarithmically with system size.

Abstract

We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. The emphasis is given on the effects of the temperature on the elementary excitations (magnetic monopoles and their Dirac strings). By using Monte Carlo techniques we calculate the specific heat, the density of poles and their average separation as functions of temperature. The specific heat and average separation between monopoles and antimonopoles exhibit a sharp peak and a local maximum, respectively, at the same temperature, $T_{p}\approx 7.2D/k_{B}$ (here, $D$ is the strength of the dipolar interaction and $k_{B}$ is the Boltzmann constant). As the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum in the average separation $d_{max}$ between oppositely charged monopoles increase logarithmically with the system size, indicating that completely isolated charges could be found only at the thermodynamic limit. In general, the results obtained here suggest that, for temperatures $T \geq T_{p}$, these systems may exhibit a phase with separated monopoles, although the quantity $d_{max}$ should not be larger than a few lattice spacings for viable artificial materials.