Field Theory for Magnetic Monopoles in (Square, Artificial) Spin Ice
Abstract
Proceeding from the more general to the more concrete, we propose an equilibrium field theory describing spin ice systems in terms of topological charges and magnetic monopoles. We show that for a spin ice on a graph, the entropic interaction in a Gaussian approximation is the inverse of the graph Laplacian matrix, while the screening function for external charges is the inverse of the screened laplacian. We particularize the treatment to square and pyrochlore ice. For square ice we highlight the gaugefree duality between direct and perpendicular structure in terms of symmetry between charges and currents, typical of magnetic fragmentation in a twodimensional setting. We derive structure factors, correlations, correlation lengths, and susceptibilities for spins, topological charges, and currents. We show that the divergence of the correlation length at low temperature is exponential and inversely proportional to the mean square charge. While in three dimension real and entropic interactions among monopoles are both 3DCoulomb, in two dimension the former is a 3DCoulomb and the latter 2DCoulomb, or logarithmic, leading to weak singularities in correspondence of the pinch points and destroying charge screening. This suggests that the monopole plasma of square ice is a magnetic charge insulator.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.03735
 Bibcode:
 2020arXiv200403735N
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Physics  Classical Physics
 EPrint:
 35 Pages, 8 figures