  We investigate the wavepacket spreading after a single spin flip in
prototypical two-dimensional ferromagnetic and antiferromagnetic quantum spin
systems. We find characteristic spatial magnon density profiles: While the
ferromagnet shows a square-shaped pattern reflecting the underlying lattice
structure, as exhibited by quantum walkers, the antiferromagnet shows a
circular-shaped pattern which hides the lattice structure and instead resembles
a classical wave pattern. We trace these fundamentally different behaviors back
to the distinctly different magnon energy-momentum dispersion relations and
also provide a real-space interpretation. Our findings point to new
opportunities for real-time, real-space imaging of quantum magnets both in
materials science and in quantum simulators.
