Spacetime Dynamics of Altermagnetic Magnons

Distinguishing altermagnetism from conventional ferromagnetism and antiferromagnetism typically relies on momentum-space probes. Here, we show that the real-space spreading of a localized spin excitation provides a distinctive dynamical fingerprint of altermagnetic order. Using linear spin-wave theory on a two-dimensional checkerboard lattice with nearest-neighbor and next-nearest-neighbor couplings J_1 and J_2, we demonstrate that finite J_2 produces direction-dependent magnon group velocities and splits the two magnon branches. The resulting propagation remains closer to that of an antiferromagnet than a ferromagnet, retaining an approximately circular outer wavefront, while the direction-dependent magnon velocities produce a pronounced cross-like spatial structure inside this front. We further show that changing the sign of J_2 to enter the unfrustrated regime (J_2<0) increases the characteristic propagation velocities and interchanges the diagonal directions of enhanced propagation, corresponding to a pi/2 rotation of the anisotropic spatial pattern. These results establish spacetime dynamics as a complementary probe of altermagnetic magnons, providing a route to identifying unconventional magnetic order through real-space propagation patterns in solid-state and synthetic quantum systems.