Inverse-design of two-dimensional magnonic crystals via topology optimization with frequency-domain micromagnetics

Abstract

Magnonic crystals (MCs) are emerging spintronic metamaterials capable of manipulating transmission properties of magnons, the quanta of spin waves. Due to the complex relationship between lattice geometry and magnonic band dispersion, it remains challenging to establish general design strategies for optimizing targeted properties in MCs. In this study, we demonstrated an inverse-design framework for two-dimensional MCs to explore unconventional lattice structures with large magnonic band gaps. We employed genetic algorithms to enable global exploration of structures with a complete band gap as the objective property, and used frequency-domain micromagnetic simulations for computationally efficient band gap evaluation. Our established inverse-design method successfully discovered several previously unreported designs of MCs, whose performance was validated using time-domain micromagnetic simulations. Furthermore, we observed that the design landscape becomes increasingly non-convex at high-order bands, suggesting the existence of multiple design solutions. The overall inverse-design framework is expected to be broadly applicable to experimentally accessible material systems and device dimensions, facilitating the formulation of design rules for MCs.

Figures (6)

• Figure 1: a) Schematic illustration of square-circular 2D MC composed of EuO matrix and Fe circular dot. Spatially discretized unit cell structure of MC and the schematic image of 1st Brillouin zone are shown below. b) Corresponding dispersion relationship calculated on unit cell shown in a). c) Conceptual schematic of the inverse-design loop implemented in this study.
• Figure 2: Algorithm chart of design optimization process
• Figure 3: a) Topological deformation of MC design during the optimization process maximizing CMBG between modes of $n=2$ and $n=3$. Note that the unit cell is expanded to $3\times3$ matrix for visualization. b) The history of change of fitness value (relative width of CMBG) along generation. c) Dispersion relationship of the best individual in 1st generation and final generation.
• Figure 4: a) Optimization results for different band numbers and corresponding dispersion relationships. b) The spatial mode profile of $\delta m_x$ at the $\Gamma$ point for the band 4-5 optimized structure.
• Figure 5: a) Schematic illustrate of broadband magnon excitation using MuMax3 simulator. The sinc pulse of magnetic field was added in the extended super cell of optimized lattice. b) FFT spectrum of excited SW for optimized structures. The vertical dashed lines represent the upper and lower frequency bounds of the band gap obtained from FD-LLG analysis.