Magnon damping and mode softening in quantum double-exchange ferromagnets

We present a comprehensive analysis of the magnetic excitations and electronic properties of {\it fully quantum} double-exchange ferromagnets, i.e., systems where ferromagnetic ordering emerges from the competition between spin, charge, and orbital degrees of freedom, but without the canonical approximation of using classical localized spins. Specifically, we investigate spin excitations within the Kondo lattice-like model, as well as a two-orbital Hubbard Hamiltonian in proximity to the orbital-selective Mott phase. Computational analysis of the magnon dispersion, damping, and spectral weight within these models reveals unexpected phenomena, such as magnon mode softening and the anomalous decoherence of magnetic excitations as observed in earlier experimental efforts, but explained here without the use of the phononic degrees of freedom. We demonstrate that these effects are intrinsically linked to incoherent spectral features near the Fermi level, which arise from the quantum nature of the local (on-site) triplets. This incoherent spectrum gives rise to a Stoner-like continuum, on which spin excitations scatter, thereby governing the magnon lifetime and significantly influencing the dynamical spin structure factor. Our study explores the transition from coherent to incoherent magnon spectra by varying the electron density. Furthermore, we demonstrate that the magnitude of the localized spin mitigates decoherence by suppressing the incoherent spectral contributions near the Fermi level. We also discuss the effective $J_1$-$J_2$ spin Hamiltonian, which can accurately describe the large doping region characterized by the softening of the magnon mode. Finally, we demonstrate that this behavior is also present in multiorbital models with partially filled orbitals, specifically in systems without localized spin moments, provided that the model operates in a strong coupling regime.