Angular-dependent spin dynamics of a triad of permalloy macrospins

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