Spin-wave eigenmodes in direct-write 3D nanovolcanoes

Extending nanostructures into the third dimension has become a major research avenue in modern magnetism, superconductivity, and spintronics, because of geometry-, curvature-, and topology-induced phenomena. Here, we introduce Co-Fe nanovolcanoes-nanodisks overlaid by nanorings-as purpose-engineered 3D architectures for nanomagnonics, fabricated by focused electron beam-induced deposition. We use both perpendicular spin-wave resonance measurements and micromagnetic simulations to demonstrate that the rings encircling the volcano craters harbor the highest-frequency eigenmodes, while the lower-frequency eigenmodes are concentrated within the volcano crater, due to the non-uniformity of the internal magnetic field. By varying the crater diameter, we demonstrate the deliberate tuning of higher-frequency eigenmodes without affecting the lowest-frequency mode. Thereby, the extension of 2D nanodisks into the third dimension allows one to engineer their lowest eigenfrequency by using 3D nanovolcanoes with 30% smaller footprints. The presented nanovolcanoes can be viewed as multi-mode microwave resonators and 3D building blocks for nanomagnonics.