“…are the equilibrium mean thermal magnon (phonon) number, with k B the Boltzmann constant and T the environmental temperature. Within the semiclassical approximation, the magnon and phonon operators are reduced to their expectation values [34,49], viz., m = m , m * = m † , b = b , and b * = b † , and the quantum noise terms can be safely dropped. In addition, the mean-field approximation by factorizing averages, i.e., m † m = m * m, is used to deal with the nonlinear term ig mb m † m. Then, the Heisenberg-Langevin equations read…”