Classifying magnons in itinerant ferromagnets from linear response TDDFT: Fe, Ni and Co revisited

The magnetic excitation spectrum of itinerant magnets exhibits rich and complex spectral features that often complicate interpretation of the underlying physics. For perturbations in the long wavelength limit, one obtains a well defined pole at zero frequency in the spectral function, the Goldstone magnon. However, for optical modes and finite wavevectors, the magnon spectrum may become damped, exhibit branching, or be completely washed out. In the present work, we show how the physical mechanism of all such features can be understood from careful analysis of the eigenmodes of the many-body spectral function. We perform first principles computations of elemental itinerant ferromagnets using a novel implementation of the linear response time-dependent density functional theory (LR-TDDFT) framework and classify the collective nature of individual spectral features based on the self-enhancement function, the product of the noninteracting Kohn-Sham susceptibility and the exchange-correlation kernel. In particular, we distinguish between coherent and incoherent collective excitations, depending on whether the real part of the self-enhancement function crosses unity at the spectral peak of the magnon, which may or may not be subject to Landau damping as quantified by the imaginary part. Classifying the computed magnon spectra accordingly, we observe coexistence of coherent magnon branches in bcc-Fe, as well as decoherence of the primary magnon branch in fcc-Ni for wave vectors near the BZ boundary where incoherent valley magnons instead carry substantial spectral weight. The analysis also naturally leads to a definition of the many-body Stoner spectrum and allows us to quantify the binding energy of the Stoner pair excitations.