Fig. 3: Quantum magnon dynamics captured by one-loop expansion and exact diagonalization.
From: Instabilities of heavy magnons in an anisotropic magnet
a, b Predictions from SU(3)-generalized non-linear spin-wave theory with one-loop order corrections (GNLSW) for the Hamiltonian of FeI2 along the experimental momentum-energy slices of Fig. 2 at 3 T and 4 T, respectively. Each panel shows in turn (left to right): kinematic conditions for decay, predicted decay rate, and realistic neutron-scattering intensity. For a single-domain of the AF structure, eight hybridized bands (En) are present: one SM and one SIBS for each of the four magnetic sublattices. These bands are numbered and color-coded to reflect their ΔSz value, which changes as a function of momentum transfer. Shaded regions indicate the extent of the two-quasiparticle continua that can be constructed from these eight quasiparticles, with a color shade (resp. gray shade) for states which do (resp. do not) yield significant decay rates. For instance, the cyan region corresponds to a 2-selection among branches E1 and/or E2. For the chosen cut direction, branches with large decay rates (red shading) may not have large spectral weight to be apparent in the calculated neutron-scattering intensity. c Magnetic field evolution of excitations calculated from Exact Diagonalization (ED) for the Hamiltonian of FeI2 on a finite cluster of 5 × 5 × 5 unit cells (500 spins) with a Hilbert space truncated to include (bottom) or not include (top) up to 4-magnon excitations. The finite-size calculation restricts the set of accessible momenta such that ED plots are for a momentum proximate to that of Fig. 2c, and slightly modifies the kinematic decay conditions compared to GNLSW calculations. d Magnetic field-dependence of the GNLSW decay rate (Lorentzian half-width at half maximum) for various branches at selected momenta.
