Exploring emergence in interconnected ferromagnetic nanoring arrays

Emergent interactions in periodic, artificial ferromagnetic nanostructures is well explored for magnetic systems such as artificial spin ices (ASI). This work presents a novel approach of an interconnected array of ferromagnetic nanorings to harness emergence in a dynamic system for functionality. Magnetic nanorings have two preferred configurations of magnetisation – ‘vortex’ that contains no domain walls (DWs) and ‘onion’ state with two DWs. In-plane applied rotating fields move DWs around a ring. The junction between interconnected rings presents a pinning potential that must be overcome to continue DW motion. In an ensemble, such as an array of interconnected rings, a sufficiently high field gives unimpeded DW motion. Under a sufficiently low field, no DWs de-pin. Both conserve DW population. Between these limits, de-pinning is probabilistic and field dependent. When one DW in an ‘onion’ state is pinned and the other de-pins, annihilation of DWs will occur and rings convert from ‘onion’ to ‘vortex’. Micromagnetic modelling also shows a DW de-pinning from a junction adjacent to a ‘vortex’ ring repopulates it with DWs. Analytical modelling of DW population revealed an equilibrium that varies non- monotonically with de-pinning probability and varies with array size and geometry. Polarised neutron reflectometry (PNR) and MOKE magnetometry measured arrays of permalloy nanorings. Magnetisation as a function of applied rotating field strength confirmed a non-monotonic response. Magnetic force microscopy (MFM) and photoemission electron microscopy (PEEM) allowed direct observation of DW configurations, revealing: highly ordered arrangements of ‘onion’ states at saturation; minor changes in DW population with low and high strength rotating fields; DW loss and breakdown in long-range order with intermediate fields. Imaging showed junctions produce behaviour analogous to emergent vertex configurations in ASIs. Interconnected nanoring arrays show good candidacy for novel computing architectures, such as reservoir computing, given their dynamic tuneability, non-linear response to an external stimulus, scalability, fading memory and repeatability.