  We applied the Self-Consistent Harmonic Approximation (SCHA), combined with
coherent states formalism, to study the ferromagnetic resonance (FMR) in a
ferromagentic/normal metal junction. Due to the interface interaction, the
FMR-generated spin current is injected from the magnetic insulator to the
normal metal, the so-called spin pumping. Ordinarily, ferromagnetic models are
described by bosonic representation or phenomenological theories; however, in a
coherent magnetization state, the SCHA is the more natural choice to treat FMR
problems. Over the years, the SCHA has successfully applied to investigate
ferro and antiferromagnetism in a wide range of scenarios. The main point of
the SCHA formalism involves the adoption of a quadratic model for which
corrections are included through temperature-dependent renormalization
parameters. Therefore, the SCHA is an efficient method for determining the
properties of magnetically ordered phases. Using the SCHA, we obtained the
temperature dependence of FMR-driven spin pumping. In addition, we found the
spin-mix conductance, the additional damping from the angular momentum
injection into the normal metal side, and the magnetic susceptibility. The SCHA
outcomes are in remarkable agreement with the results of the literature.
