Soft spin waves triggering macrospin reversals in isolated nodes of Kagome-like networks

We investigate the spin wave dynamics involved in the magnetization reversal process for a simple, three-macrospin node that is a key geometrical ‎element of many networks, such as kagome or honeycomb lattices. In particular, we study the correlation between soft mode profile and order of reversal of the different macrospins, in the perspective of predicting the occurrence of Dirac strings in actual kagome lattices. The dynamical matrix method is used to compute the spin wave modes. We look for an experimental confirmation of the main features found by theory: three-macrospin nodes were fabricated by ‎standard electron beam lithography, and consist of 15-nm-thick, elongated ellipses (aspect ratio 2.5) ‎made of Permalloy, which interact via dipole-only interactions (disconnected at the node). DC magnetization curves were obtained using SQUID ‎magnetometry, from which we could check the presence of discontinuities in correspondence to any macrospin reversal. Broad-‎band FMR measurements were obtained using a meander-line or a strip-line antenna, showing good agreement with the theoretical curves. We consider also a three-macrospin node with an asymmetric geometry, in which a macrospin has a reduced ‎aspect ratio: we show the peculiar features in magnetization loops and FMR measurements, and their correspondence with the theoretical predictions. Work at Argonne was supported by U.S. DOE, Office of Science, DMSE. Work at Northwestern was supported under U.S. NSF Grant 1507058. Work at Kentucky was supported by U.S. NSF Grant DMR-1506979.