Spin wave interactions in the pyrochlore Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

Abstract

We study the effect of magnon interactions on the spin wave spectra of the all-in-all-out phase of the pyrochlore nearest neighbour antiferromagnet with a Dzyaloshinskii-Moriya interaction ($D$). The leading order corrections to spin wave energies indicate a significant renormalisation for commonly encountered strengths of the Dzyaloshinskii-Moriya term. For low values of $D$ we find a potential instability of the phase itself, indicated by the renormalisation of magnon frequencies to negative values. We have also studied the renormalized spectra in the presence of magnetic fields along three high symmetry directions of the lattice, namely the $[111]$, $[100]$ and $[110]$ directions. Generically, we find that for a fixed value of the Dzyaloshinskii-Moriya interaction renormalized spectra for the lowest band decrease with an increasing strength of the field. We have also analyzed the limits of the two magnon continuum and probed the possibility of magnon decay. For a range of $D$ and the field strength we identify possible parameter regimes where the decay of the higher bands of the system are kinematically allowed.

This version is close to the published version in Phys. Rev. B. The text has been expanded at several places and more steps/expressions have been provided explicitly for clarity. An addition to the analysis classical ground states pertaining to the field dependence of canting angles is presented in the Appendix

References in corpus (24)

• Magnetic Pyrochlore Oxides
• Observation of the Magnon Hall Effect
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Spontaneous Magnon Decays
• Spin-waves in triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities
• Dirac magnons in honeycomb ferromagnets
• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Damped Topological Magnons in the Kagomé-Lattice Ferromagnets
• Flat spin wave dispersion in a triangular antiferromagnet
• Interaction-stabilized topological magnon insulator in ferromagnets
• Instability of antiferromagnetic magnons in strong fields
• Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films
• Weyl magnons in pyrochlore antiferromagnets with all-in-all-out orders
• Topological magnons with nodal-line and triple-point degeneracies: Implications for thermal Hall effect in pyrochlore iridates
• Field-induced dynamical properties of the $XXZ$ model on a honeycomb lattice
• Topological magnetic excitations
• Magnon interactions in the frustrated pyrochlore ferromagnet Yb${}_2$Ti${}_2$O${}_7$
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Interacting topological Dirac magnons
• Temperature-Induced Magnonic Chern Insulator in Collinear Antiferromagnets
• Magnon-magnon interaction in monolayer MnBi${}_2$Te${}_4$
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Magnon bands in pyrochlore slabs with Heisenberg exchange and anisotropies