Configurational Effects in Ferromagnetic Resonance Spectra of Clusters of Macrospins

We present experimental and theoretical investigations of spin wave modes in Permalloy (Ni80Fe20) macrospin arrays in cross and square configurations to understand the dynamics among clusters of them. These configurations are periodically patterned at the central signal line of a coplanar waveguide to acquire strong coupling with the microwave field. Their dynamic behavior is analyzed using broadband ferromagnetic resonance (FMR) measurements. Our results reveal a notable mode-splitting associated with a rotation of the macrospin configuration, highlighting the influence of the geometry on spin wave excitations. Furthermore, the spectra depend on the macrospin configuration as evidenced by the discontinuity of the FMR curves associated with different magnetization reversal fields, and the interaction between modes at low frequency. Theoretical calculations support the experimental observations of fundamental modes and mode-splitting at the vertex region. These findings contribute to the development of artificial spin ice (ASI) for functional magnonic networks and spin-based computing applications.