Nonreciprocal Interactions Reshape Topological Defect Annihilation

We show how nonreciprocal ferromagnetic interactions between neighboring planar spins in two dimensions, affect the behavior of topological defects. Nonreciprocity is introduced by weighting the coupling strength of the two-dimensional XY model by an anisotropic kernel. As a consequence, in addition to the topological charge q, the actual shape of the defects becomes crucial to faithfully describe their dynamics. Nonreciprocal coupling twists the spin field, selecting specific defect shapes, dramatically altering the pair annihilation process. Defect annihilation can either be enhanced or hindered, depending on the shape of the defects concerned and the degree of nonreciprocity in the system. We introduce a continuous description-for which the phenomenological coefficients can be explicitly written in terms of the microscopic ones-that captures the behavior of the lattice model.