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

TL;DR

This paper investigates how magnon interactions and Dzyaloshinskii-Moriya interactions influence the spin wave spectra of a pyrochlore antiferromagnet, revealing significant renormalizations, potential phase instabilities, and conditions for magnon decay.

Contribution

It provides a detailed analysis of magnon interaction effects on spin wave spectra in the presence of Dzyaloshinskii-Moriya interactions and magnetic fields, highlighting potential phase instabilities and magnon decay regimes.

Findings

Significant renormalization of spin wave energies due to magnon interactions.

Potential instability of the all-in-all-out phase at low Dzyaloshinskii-Moriya interaction values.

Identification of parameter regimes where magnon decay is kinematically allowed.

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.