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This review presents a comprehensive study of the spatial dispersion ofpropagating magnons electrically emitted in extended yttrium-iron garnet (YIG)films by the spin transfer effects across a YIG$\vert$Pt interface. Our goal isto provide a generic framework to describe the magnon transconductance insidemagnetic films. We experimentally elucidate the relevant spectral contributionsby studying the lateral decay of the magnon signal. While most of the injectedmagnons do not reach the collector, the propagating magnons can be split intotwo-fluids: \textit{i)} a large fraction of high-energy magnons carrying energyof about $k_B T_0$, where $T_0$ is the lattice temperature, with acharacteristic decay length in the sub-micrometer range, and \textit{ii)} asmall fraction of low-energy magnons, which are particles carrying energy ofabout $\hbar \omega_K$, where $\omega_K/(2 \pi)$ is the Kittel frequency, witha characteristic decay length in the micrometer range. Taking advantage oftheir different physical properties, the low-energy magnons can become thedominant fluid \textit{i)} at large spin transfer rates for the bias causingthe emission of magnons, \textit{ii)} at large distance from the emitter,\textit{iii)} at small film thickness, or \textit{iv)} for reduced bandmismatch between the YIG below the emitter and the bulk due to variation of themagnon concentration. This broader picture complements part I \cite{kohno_SD},which focuses solely on the nonlinear transport properties of low-energymagnons.

Non-local magnon transconductance in extended magnetic insulating films.\\Part II: two-fluid behavior