  This review provides a comprehensive study of the nonlinear transport
properties of magnons, which are electrically emitted or absorbed inside
extended YIG films by spin transfer effects via a YIG$\vert$Pt interface. Our
purpose is to experimentally elucidate the pertinent picture behind the
asymmetric electrical variation of the magnon transconductance analogous to an
electric diode. The feature is rooted in the variation of the density of
low-lying spin excitations via an electrical shift of the magnon chemical
potential. As the intensity of the spin transfer increases in the forward
direction (regime of magnon emission), the transport properties of low-energy
magnon go through 3 distinct regimes: \textit{i)} at low currents, where the
spin current is a linear function of the electrical current, the spin transport
is ballistic and set by the film thickness; \textit{ii)} for amplitudes of the
order of the damping compensation threshold, it switches to a highly correlated
regime limited by magnon-magnon relaxation process and marked by a saturation
of the magnon transconductance. Here the main bias, that controls the magnon
density, are thermal fluctuations beneath the emitter. \textit{iii)} As the
temperature under the emitter approaches the Curie temperature, scattering with
high-energy magnons dominates, leading to diffusive transport. We note that
such sequence of transport regimes bears analogy with electron hydrodynamic
transport in ultra-pure media predicted by Radii Gurzhi. This study restricted
to low energy part of the magnon manifold complements part II of this
review\cite{kohno_2F}, which concentrates instead on the whole spectrum of
propagating magnons.
