  Conductivities are key material parameters that govern various types of
transport (electronic charge, spin, heat etc.) driven by thermodynamic forces.
Magnons, the elementary excitations of the magnetic order, flow under the
gradient of a magnon chemical potential in proportion to a magnon (spin)
conductivity $\sigma_{m}$. The magnetic insulator yttrium iron garnet (YIG) is
the material of choice for efficient magnon spin transport. Here we report an
unexpected giant $\sigma_{m}$ in record-thin YIG films with thicknesses down to
3.7 nm when the number of occupied two-dimensional (2D) subbands is reduced
from a large number to a few, which corresponds to a transition from 3D to 2D
magnon transport. We extract a 2D spin conductivity ($\approx1$ S) at room
temperature, comparable to the (electronic) spin conductivity of the
high-mobility two-dimensional electron gas in GaAs quantum wells at millikelvin
temperatures. Such high conductivities offer unique opportunities to develop
low-dissipation magnon-based spintronic devices.
