Characteristics of magnon-phonon coupling in magnetic insulator based on the Boltzmann equation

The magnon, an elementary excitation of an orderly magnetic system, is currently receiving substantial attention due to its excellent spin transmission properties. Researchers have observed a clear correlation between magnon transport properties and temperature. Existing theories do include the influence of temperature, but cannot clearly explain many phenomena, including a detected abnormal negative signal. In this article, we build a new magnon transport theory based on the Boltzmann method, which incorporates a magnetic field-induced "anti-diffusion " driving term, a magnon-phonon interaction induced thermal driving term, and diverse scattering terms, such as a scattering process which leads magnons to a special state with a collective velocity. We claim that collective velocity is the crucial factor in producing an abnormally negative signal. We formulated an equation capturing the system's spin properties, which we solved. Our results qualitatively explain the abnormal phenomenon observed in experiments.