Spontaneous magnon decay in two-dimensional altermagnets

We show that magnons in two-dimensional altermagnets can spontaneously decay at zero temperature. The decay rate is determined by quantum fluctuations and scattering processes involving the decay of a single magnon into three. These processes are kinematically allowed due to the convexity of the altermagnetic magnon dispersion. For small wave vectors <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>k</a:mi></a:math>, the decay rate is proportional to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mi>k</b:mi><b:mn>5</b:mn></b:msup></b:math> with a direction-dependent prefactor, which is maximal along the diagonals of the Brillouin zone. Moreover, for a given momentum only magnons with one specific chirality can spontaneously decay.