Magnon-magnon interaction and magnon relaxation time in a ferromagnetic Cr2Ge2Te6 monolayer

Despite the intense amount of attention and huge potential of two-dimensional (2D) magnets for applications in novel magnetic, magneto-optical, magnetothermal, and magnetoelectronic devices, there is a lack of robust strategy developed to systematically understand magnon-magnon interactions (MMIs) at finite temperature. In this paper, we present a first-principles theoretical method to introduce the finite temperature magnon-magnon interaction into a Heisenberg Hamiltonian through a correction energy. Wick's theorem is used to decouple the four-magnon operators to two-magnon order. We demonstrate the capabilities of this method by studying the strength of MMI in a Cr2Ge2Te6 monolayer. The spin-wave spectrum at finite temperature and the time-dependent spin autocorrelation function are explored. It is found that the magnon relaxation time due to magnon-magnon scattering increases with temperature because of the reduction in magnon energy, while it decreases with wave vector and external magnetic field. Our results provide insight into understanding the magnon damping and energy dissipation in two-dimensional ferromagnetic materials.