Magnetostatic dipolar domain-wall pinning in chains of permalloy triangular rings

In a combined experimental and numerical study, we investigated the details of the motion and pinning of domain walls in isolated and interacting permalloy triangular rings (side 2 mu m, width 250 nm, and thickness 25 nm). To induce interaction between the rings, they were arranged either in vertical chains with an apex of each triangle in proximity to the edge center of the triangle above it or in horizontal chains where the proximity is between the adjacent corners of the triangles. Using longitudinal and diffraction magneto-optic Kerr effects, magnetic force microscopy, and micromagnetic simulations, we determined the field dependence of the spin structure in the rings. In all cases the remnant state of each ring is an "onion" state characterized by two domain walls-one head to head the other tail to tail-pinned at the apexes. In isolated rings the magnetization reversal occurs between two onion states via the formation of an intermediate vortex state, which arises from the motion and annihilation of the two domain walls. In the case of the horizontal chains the reversal mechanism is unchanged except that the dipolar interaction affects the field range in which the rings are in the vortex state. In the case of vertical chains an additional intermediate state is observed during reversal. The new state involves a domain wall pinned at the center of the edge that is in close proximity to the apex of its neighbor. We show that the domain-wall motion in this last case can be modeled by a triple potential well. Because the new state requires that a domain wall be pinned at the neighboring apex, our observations can be viewed as a very elementary form of magnetic logic.