Gyroid ferromagnetic nanostructures in 3D magnonics

This research chapter provides a comprehensive overview of ferromagnetic gyroidal nanostructures, combining a review of state-of-the-art research with our new findings on their implications for 3D magnonics. Both static and dynamic magnetization studies show that non-trivial shape anisotropy, chirality, and inhomogeneous demagnetization fields influenced by specific crystallographic arrangements lead to multiple low-energy state magnetization textures, spin-wave mode localization, and controllable spin-wave propagation, highlighting the substantial potential of gyroidal nanostructures. The review integrates insights into micro/nano texturing to elucidate the intricate relationships between gyroidal geometry, chirality, and their effective magnetic properties, especially at microwave frequencies. Our study of resonance frequencies in gyroid samples under rotational field manipulation further reveals the significant influence of geometric anisotropy on ferromagnetic resonance signal strength. This chapter establishes a fundamental understanding of ferromagnetic gyroidal nanostructures, paving the way for their future investigation in 3D magnonics.

💡 Research Summary

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The chapter “Gyroid Ferromagnetic Nanostructures in 3D Magnonics” provides a comprehensive review of the state‑of‑the‑art research on gyroid‑based three‑dimensional (3D) magnonic crystals (MCs) and presents new experimental and simulation results that illuminate their unique static and dynamic magnetic properties. The authors begin by situating spin‑wave (SW) research at the intersection of magnonics and spintronics, emphasizing the need for low‑loss, high‑frequency signal carriers that avoid Joule heating. While most magnonic crystals to date are planar (2D) thin‑film structures with largely homogeneous magnetization across the thickness, the introduction of a third dimension adds a rich set of degrees of freedom: geometry, topology, crystallographic orientation, and the resulting inhomogeneous demagnetization fields.

The gyroid is described as a triply periodic minimal surface belonging to the I4₁32 (No. 214) space group, characterized by zero mean curvature, chiral triple junctions, and a body‑centered cubic lattice. Its mathematical representation (a trigonometric inequality) allows precise control of the volume filling fraction ϕ, which directly tunes the size of the interconnected channels and the curvature of the surfaces. The authors discuss several fabrication routes that have recently become viable: block‑copolymer self‑assembly to generate a gyroid template, two‑photon lithography for high‑resolution 3D patterning, focused electron‑beam deposition for metal filling, and subsequent annealing steps. By varying ϕ from 0 % to ~30 %, the channel diameter, wall thickness, and overall magnetic anisotropy can be systematically adjusted.

Static micromagnetic simulations reveal that the gyroid’s chiral geometry induces multiple low‑energy magnetization textures (vortex‑like, helical, and domain‑wall configurations) that coexist within a single sample. The external magnetic field direction acts as a selector among these states; rotating the field around the crystal axes triggers abrupt changes in the ferromagnetic resonance (FMR) spectra, both in resonance frequency and signal amplitude. This demonstrates a strong coupling between geometric anisotropy and the effective magnetic field landscape.

Dynamic investigations focus on spin‑wave mode localization. The classic Damon‑Eshbach (DE) surface mode appears on gyroid surfaces where the propagation vector is perpendicular to the in‑plane component of the applied field, leading to non‑reciprocal excitation and detection. In addition, static demagnetization fields generate edge‑localized modes that travel along the gyroid’s internal “edges” where the internal field is reduced. The curvature of the gyroid channels further confines SWs, producing volume‑localized modes in the channel cores. Importantly, the chiral network acts as a topologically protected waveguide: spin waves can follow highly curved paths without back‑scattering, a behavior linked to non‑trivial Chern numbers and higher‑order topological invariants. While higher‑order topological corner states have been observed in 2D antiskyrmion crystals, the gyroid provides a 3D platform where such phenomena could be explored.

The authors also discuss the impact of the gyroid’s geometry on magnonic band structures. By adjusting the lattice constant and filling fraction, band gaps can be opened or closed, and the effective damping becomes strongly wave‑vector dependent. This tunability is crucial for designing reconfigurable magnonic devices that can switch between different operational regimes (e.g., broadband transmission vs. narrowband filtering) simply by rotating an external field or by applying a modest strain.

In the outlook, the chapter argues that gyroidal ferromagnetic nanostructures are uniquely positioned to advance 3D magnonics. Their combination of low loss at microwave to sub‑THz frequencies, strong geometric anisotropy, and inherent chirality enables the realization of spin‑wave‑based logic gates, non‑linear frequency converters, and directional waveguides with unprecedented robustness. Moreover, the ability to engineer the volume filling fraction and to manipulate the external field in situ offers a pathway toward fully reconfigurable magnonic circuits, where band structures, propagation direction, and mode localization can be dynamically programmed. The authors conclude that further experimental work—particularly on time‑resolved imaging of spin‑wave propagation in gyroid networks and on the exploration of higher‑order topological states—will be essential to unlock the full potential of these fascinating 3D magnonic crystals.