  Harnessing high-frequency spin dynamics in three-dimensional (3D)
nanostructures may lead to paradigm-shifting, next generation devices including
high density spintronics and neuromorphic systems. Despite remarkable progress
in fabrication, the measurement and interpretation of spin dynamics in complex
3D structures remain exceptionally challenging. Here we take a first step and
measure coherent spin waves within a 3D artificial spin ice (ASI) structure
using Brillouin light scattering. The 3D-ASI was fabricated by using a
combination of two-photon lithography and thermal evaporation. Two spin-wave
modes were observed in the experiment whose frequencies showed a monotonic
variation with the applied field strength. Numerical simulations qualitatively
reproduced the observed modes. The simulated mode profiles revealed the
collective nature of the modes extending throughout the complex network of
nanowires while showing spatial quantization with varying mode quantization
numbers. The study shows a well-defined means to explore high-frequency spin
dynamics in complex 3D spintronic and magnonic structures.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons