Propagation of magnetic charge monopoles and Dirac flux strings in an artificial spin-ice lattice

We systematically investigate magnetic reversal of permalloy islands in a square spin-ice geometry with in situ Lorentz microscopy. Differential phase imaging reveals the presence of a flux channel similar to a Dirac string between the magnetic charge monopoles during the reversal. Analysis of the phase images shows that positively and negatively charged monopoles always move together with the flux channel. Statistical analysis of monopole populations and system correlations shows the emergence of a highly frustrated state for low magnetizations. This state is explained by a strong influence of charge ordering, which limits monopole densities.