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-ferromagnets Mn$_3$Rh using linear response time-dependent density functional theory. To this end, we present a novel first principles approach relying on the evaluation of dynamical susceptibility based on the non-collinear KKR Green's functions method. This approach enables us not only to treat spin and charge dynamics on an equal footing but also address the Landau damping of spin waves being inaccessible to adiabatic methods. Our calculations reveal three distinct Goldstone modes dispersing linearly in the long-wavelength regime. We discuss their non-trivial polarizations and proceed to an in-depth analysis of their Landau damping. The spin-waves turn out to be defined in the whole Brillouin zone but their damping become substantial away from the zone's center.

Figures (4)

• Figure 1: Left: Magnetic unit cell of the TAF Mn$_3$X with the Mn atoms depicted in color depending on their orientation and the X (Rh,Ir,Pt) atoms in grey. The (111) plane is marked in light blue. Arrows show the magnetic moment directions. Right: The top view on the (111) plane reveals the characteristic frustrated kagome lattice.
• Figure 2: Contribution of the magnetic Mn atoms to the total band structure. Colour depicts the magnetization direction within the (111) plane, whereas intensity shows the density of states.
• Figure 3: Left: Magnon dispersion and inverse lifetimes (shown as bars designating the full with at half-maximum, FWHM, of the magnon peak) of TAF Mn$_3$Rh obtained from our LRTDDFT calculations. The insets show the shapes magnon modes for selected momenta and a sketch of the 2D Brillouin zone, combined with the corresponding Fermi surface. The precessing moments' trajectories are colour-coded like the dispersions of different modes. Right: Magnons' FWHMs as a function of their energy, along the M-$\Gamma$-M' path.
• Figure 4: Landau maps for selected momenta (columns) and all three magnon polarization (rows). Shown is the spectral density of occupied electronic states with the initial momentum ${\mathbf k}$ within Stoner pairs contributing to the damping of magnon with momentum ${\mathbf q}$. The final states reside within bands above the Fermi energy and feature momentum ${\mathbf k} + {\mathbf q}$. For clarity, only momenta in the (111) plane are shown. All maps are normalized to the maximum value per BZ point.