  We present a quantum Hall effect of magnons in two-dimensional clean
insulating magnets at finite temperature. Through the Aharonov-Casher effect, a
magnon moving in an electric field acquires a geometric phase and forms Landau
levels in an electric field gradient of sawtooth form. At low temperatures, the
lowest energy band being almost flat carries a Chern number associated with a
Berry curvature. Appropriately defining the thermal conductance for bosons, we
find that the magnon Hall conductances get quantized and show a universal
thermomagnetic behavior, i.e., are independent of materials, and obey a
Wiedemann-Franz law for magnon transport. We consider magnons with quadratic
and linear (Dirac-like) dispersions. Finally, we show that our predictions are
within experimental reach for ferromagnets and skyrmion lattices with current
device and measurement techniques.
