Dispersion and lifetimes of magnons in non-collinear magnets from time dependent density functional theory

Abstract

We investigate the spin dynamics of the non-collinear kagome triangular anti-ferromagnet Mn$_3$Rh using linear response time-dependent density functional theory. To this end, we present a novel first principles computational scheme for the evaluation of the dynamical susceptibility based on the non-collinear KKR Green's functions method and a symbolic computer algebra.This approach allows us to address the Landau decay of spin waves into non-collinear electron-hole Stoner pairs being inaccessible to adiabatic methods. Our calculations reveal three distinct Goldstone modes dispersing linearly in the long-wavelength regime giving rise to the three magnon branches and we discuss their non-trivial spatial polarizations. The spin-waves turn out to be defined in the whole Brillouin zone but their Landau damping becomes substantial away from the zone's center. Surprisingly, magnons of comparable momenta and energies can feature, depending on their chirality, considerably different attenuation, in some cases of predominantly resonant character. We trace this effect to the interplay between the magnon eigenvectors and the intrinsically spin-polarized altermagnetic band structure and the resulting spectrum of non-collinear Stoner states.