Geometry driven intermediate states in artificial square ice structures

Abstract Conventional approaches to studying nanomagnets often focus on the energetic relaxation from an initialized state to a final low-energy state, typically assuming a single spin-flip regime. This relaxation process inherently involves intermediate states with variable magnetostatic energies, which influence the probability of reaching specific final configurations. Here, we investigate the nature of intermediate states in a simple nanomagnet model consisting of four nanomagnets arranged onto a square plaquette. Through systematic exploration, we demonstrate how geometry influences energy relaxation pathways via multipolar analysis. We elaborate on the nature of energy relaxation pathways, with direct consequences for understanding magnetic frustration and metastability in artificial spin ice structures. Our theoretical models are supported by experimental results from field-induced relaxation using Magnetic Force Microscopy measurements. This work provides an intuitive framework for understanding energy relaxation in artificial spin ice structures.