Domain wall motion underpins emerging spintronic technologies, such as high-speed racetrack devices and THz logic, and accelerating walls quickly is a key challenge on the path to faster devices. Recent experimental advances introduced magnetic materials with nonuniform composition, allowing angular momentum compensation points and fast domain wall motion, although acceleration of domain walls in these materials remains poorly understood. Here, we show that spatial variation of exchange and anisotropy not only pushes the wall toward a lower wall surface tension region, but also modifies its inertial mass, giving rise to a variable-mass relativistic dynamics. We find another force, originating from the magnon velocity gradient, that dominates as the wall velocity approaches the magnon speed. Our results identify domain walls in nonuniform magnets as a playground for relativistic physics with variable mass and limiting speed.

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• Antiferromagnetism
• Domain walls
• Ferrimagnetism
• Ferromagnetism
• Magnetization dynamics
• Magnetization switching
• Micromagnetism
• Spin dynamics