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

Abstract

We study the spin dynamics in arrays of densely packed submicron Ni${}_{80}$Fe${}_{20}$ 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 ${H}_{\mathrm{mr}}$. 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, ${H}_{\mathrm{mr}}$ is found to vary characteristically as a function of the width difference $\ensuremath{\Delta}w$ of neighboring wires. Interestingly, the sign of ${H}_{\mathrm{mr}}$ reflects the orientation of the wires' magnetization. For our devices we find experimentally frequency splittings $\ensuremath{\delta}f$ 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 $\ensuremath{\delta}f$ for different geometrical parameters such as the edge-to-edge separation $a$ and the width difference $\ensuremath{\Delta}w$. Though relevant for ${H}_{\mathrm{mr}}$, $\ensuremath{\Delta}w$ is not decisive for $\ensuremath{\delta}f$. 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.