Interacting Dirac magnons in the van der Waals ferromagnet CrBr3

We study the effects of magnon-magnon interactions in the two-dimensional van der Waals ferromagnet <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>CrBr</a:mi><a:mn>3</a:mn></a:msub></a:math> focusing on its honeycomb lattice structure. Motivated by earlier theoretical predictions of temperature-induced spectral shifts and van Hove singularities in the magnon dispersion [S. S. Pershoguba , ], we go beyond the commonly used thermal magnon approximation by applying second-order perturbation theory in a fully numerical framework. Our analysis uncovers significant deviations from previous analysis: in particular, the predicted singularities are absent, consistent with recent inelastic neutron scattering measurements [S. E. Nikitin , ]. Moreover, we find that the temperature dependence of the renormalized magnon spectrum exhibits a distinct <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mi>T</b:mi><b:mn>3</b:mn></b:msup></b:math> behavior for the optical magnon branch, while retaining <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mi>T</c:mi><c:mn>2</c:mn></c:msup></c:math> behavior for the acoustic or down magnon band. This feature sheds light on the collective dynamics of Dirac magnons and their interactions. We further compare the honeycomb case with a triangular Bravais lattice, relevant for ferromagnetic monolayer <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>MnBi</d:mi><d:mn>2</d:mn></d:msub><d:msub><d:mi>Te</d:mi><d:mn>4</d:mn></d:msub></d:mrow></d:math>, and show that both systems lack singular features while displaying quite distinct thermal trends.