This paper presents a comprehensive study of the nonlinear transport properties of magnons electrically emitted or absorbed in extended yttrium-iron garnet (YIG) films by the spin transfer effect across a $\mathrm{YIG}|\mathrm{Pt}$ interface. Our goal 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-wave modes (so-called low-energy magnons) via an electrical shift of the magnon chemical potential. As the intensity of the spin transfer increases in the forward direction (magnon emission regime), the transport properties of low-energy magnons pass through three distinct regimes: (i) at low currents, where the spin current is a linear function of the electric current, the spin transport is ballistic and determined by the film thickness; (ii) for amplitudes of the order of the damping compensation threshold, it switches to a highly correlated regime, limited by the magnon-magnon scattering process and characterized by a saturation of the magnon transconductance. In other words, the reported signal suggests coupled dynamics between numerous modes rather than Bose-Einstein condensation around a single dominant mode. (iii) As the temperature under the emitter approaches the Curie temperature, scattering with high-energy magnons starts to dominate, leading to diffusive transport. We find that such a sequence of transport regimes is analogous to the electron hydrodynamic transport in ultrapure media predicted by Radii Gurzhi, where condensation of magnons. This study, restricted to the low-energy part of the magnon manifold, complements Paper II [Kohno et al., Phys. Rev. B 108, 144411 (2023)] of this series, which focuses on the full spectrum of propagating magnons.

• Received 10 October 2022
• Revised 2 June 2023
• Accepted 25 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.144410