We experimentally and theoretically characterize the angular dependent microwave response of three-macrospin-vertex structures that can serve as a node in various spin ice lattices. The macrospins consist of patterned permalloy thin films with an elliptical cross-section together with an in-plane aspect ratio allowing an Ising-like behavior together with bulk modes as low-frequency excitations in the field range of interest. Various branches of the frequency-magnetic field curves display atypical behaviors and discontinuities, together with softening due to macrospin reversals. The overall behavior observed accurately corresponds to a superposition of the spectra of the individual macrospins. The measured ferromagnetic resonance spectra are in good agreement with theoretical modeling. In particular, they reveal a close correlation between the field direction (relative to the individual macrospins), and the corresponding frequency-magnetic field curve; i.e., between the geometry and the magnetic response.
We theoretically and experimentally investigate magnetization reversal and associated spin wave dynamics of isolated threefold vertices that constitute a Kagome lattice. The three permalloy macrospins making up the vertex have an elliptical cross section and a uniform thickness. We study the dc magnetization curve and the frequency vs. field curves (dispersions) of those spin wave modes that produce the largest response. We also investigate each macrospin reversal from a dynamic perspective, by performing micromagnetic simulations of the reversal processes, and revealing their relationships to the soft mode profile calculated at the equilibrium state immediately before reversal. The theoretical results are compared with the measured magnetization curves and FMR spectra. The agreement achieved suggests that a much deeper understanding of magnetization reversal and accompanying hysteresis can be achieved by combining theoretical calculations with static and dynamic magnetization experiments.
We present experimental and theoretical studies of spin-wave mode dynamics in artificial Kagome spin ice vertices made of three identical 15-nm thick elongated Ni80Fe20 nano-islands (macrospins). We consider several possible configurations, from completely disjointed macrospins (full dipolar inter-element interactions) to fully jointed macrospins (full dipolar-exchange interactions). Using angular-resolved magnetic field dependent broadband ferromagnetic resonance (FMR), we demonstrate the occurrence of a mode localized in the vertex region as indicated by the distinct behavior of the FMR spectra at different angles and configurations. Theoretical calculations using micromagnetic simulations support the existence, origin, and behavior of this mode by interpreting it as a localized, quasi-uniform Kittel mode. Our findings pave the way for designing the most appropriate network consisting of ferromagnetic nanomagnets for specific application purposes in magnonics.
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