Field- and geometry-controlled avoided crossings of spin-wave modes in reprogrammable magnonic crystals

We study the spin dynamics in arrays of densely packed submicron Ni₈₀Fe₂₀ wires which form one-dimensional magnonic crystals. They are subject to an in-plane magnetic field H being collinear with the wires. In the case when neighboring wires are magnetized antiparallel, broadband spin-wave spectroscopy reveals a mode repulsion behavior around a certain field Hₘᵣ. We attribute this to dipolar coupling and avoided crossing of resonant modes of individual wires. The modes are found to hybridize across the array and form acoustic and optical modes. When an array of alternating-width wires is considered, Hₘᵣ is found to vary characteristically as a function of the width difference Δw of neighboring wires. Interestingly, the sign of Hₘᵣ reflects the orientation of the wires' magnetization. For our devices we find experimentally frequency splittings δf on the order of 1 GHz between the acoustic and optical mode. We use micromagnetic modeling to analyze spin precession profiles and investigate the hybridization of modes. The simulated splitting is larger than the observed one. We attribute the discrepancy to a reduced dipolar coupling in the real samples. Using a theoretical model which considers the reduced dipolar coupling we analyze δf for different geometrical parameters such as the edge-to-edge separation a and the width difference Δw. Though relevant for Hₘᵣ, Δw is not decisive for δf. Instead, a is key for the frequency splitting. The results are relevant in order to tailor the dynamic response and band structure of magnonic crystals.