Reconstruction of magnon eigenfunctions by X-ray magnetic vector chronoscopy

The collective precession of magnetization manifests itself as magnon modes. These modes are governed by complex-valued vectorial eigenfunctions, which have remained experimentally challenging to observe. Here we introduce X-ray magnetic vector chronoscopy (XMVC), a time-resolved resonant scattering method that reconstructs the full magnetization dynamics with angular resolution of 0.1° (±0.01°). Applied to a synthetic antiferromagnetic multilayer (Si/NiFe (8 nm)/Ru (0.8 nm)/CoFeB (5.5 nm)), XMVC enables magnon state tomography, by directly measuring the nanoscale vectorial eigenfunctions of hybridized modes arising from magnon-magnon coupling. This approach provides full access to the system's non-Hermitian Hamiltonian, revealing the complex-valued coupling strengths and non-orthogonal eigenbases. These results establish XMVC as an experimental platform for studying nanoscale spin systems by extracting the eigenfunctions of the system.