Artificial spin ices (ASI) are arrays of nanoscale magnets, usually arranged in frustrated geometries. Among the ASI, the kagome geometry (AKSI) has been extensively studied and considered to explore a wide range of interesting Physics phenomena, including mimicking bulk spin ice materials, and acting as a metamaterial for applications in magnonics 1.
The goal of this work is to study the global and local spatial dependence of the coercivity of a Permalloy AKSI (20 nm thick elliptical magnetic islands). The magnetization curves were acquired by magneto-optic Kerr effect measurements with the laser spot adjusted for the required purpose (either global or local). The angular dependence of coercivity exhibits a periodic behavior with a period of 60°, which reflects the symmetry of the underlying honeycomb pattern. The coercivity values vary from ~120 Oe to ~145 Oe, resulting in a peak-to-peak amplitude of ~25 Oe. The minima (maxima) occur when the applied field is perpendicular (parallel) to the magnet's long axis. This result agrees with the fact that the long axis direction being an easy axis of a single nanomagnet. A 20 nm permalloy continuous thin film with similar lateral dimensions as the AKSI lattice shows a nearly constant coercivity around only a few Oe. This indicates that the higher magnitude of the AKSI coercivity is due to the thin film patterning. On the other hand, it is well known that small systems with long range order interactions exhibit pronounced size effects, intuitively understood from the fact that long range interactions are limited by the sample size 2. By controlling the position of the laser spot to 2 um nominal diameter it was possible to scan the whole sample and determine a spatial map of the coercivity, where each point of the map corresponds to a distinct subregion of the lattice. The results clearly show that the magnetisation reversal properties are locally affected depending on how close to the edge the hysteresis loop is measured. A continuous decrease of the coercive fields close to the array edges reveals that surface effects are present in AKSI and, in principle, could be explained in the light of translation symmetry breaking in systems with long range order interactions.
References:
1 S. Skjærvø, H. Christopher and R. Stamps, Nature Reviews, Vol. 2, p. 13 (2020).
2 K. Binder and P. C. Hohenberg, Phys. Rev. B, Vol. 6, p. 3461 (1972).