Nambu monopoles interacting with lattice defects in a two-dimensional artificial square spin ice

The interactions between an excitation (similar to a pair of Nambu monopoles connected by their associated string) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the ``imperfect'' island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We show that the two extreme points of a defective island behave like two opposite magnetic charges. Then, the effective interaction between a pair of Nambu monopoles with the defective island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.