Spin wave and magnetic domain wall are two of basic excitations in magnetic systems, and their spatiotemporal interplay encodes rich information of underlying magnetic interactions. In synthetic antiferromagnets, the domain wall acquires an inertia and the spin wave unlocks the full polarization degree of freedom, lays a salient platform for their interplay. Here we show that both the translational and angular velocities of the domain wall in synthetic antiferromagnets can be detected via the scattered spin wave, through the synergy of translational and angular Doppler effects. Following the setup of an electromagnetic or acoustic radar, the time evolution of a domain wall state is accessible via a series of spin wave packets, in both noninvasive and invasive fashion. The inspections in the frequency domain, offer new paradigms in the exploration and exploitation of magnetic excitations.

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• Domain walls
• Frequency conversion
• Radar
• Spin waves
• Synthetic antiferromagnetic multilayers