Magnon decays in magnets with long-range interactions

A recent experimental study realized long-range XY order in a ferromagnet at finite temperature using a 2D Rydberg atom array. To prepare this XY ordered state, a staggered magnetic field was applied; we aim to understand the effect of this staggered field on magnon decay rates and on spin correlations, and how the 1/r³ ("dipolar") interactions affect the kinematics of magnon decay. Using spin-wave theory to study the dipolar XY ferromagnet and antiferromagnet on the square lattice, we focus on (i) the kinematics of magnon decay and (ii) the magnon decay vertices. A field-independent region of kinematically allowed field-induced decays, dictated by the lattice symmetry, is observed. Cubic vertices are used to calculate magnon self-energies, which can then be used to calculate spin correlation functions.