The coherent magnon state representation is employed to investigate the quantum-statistical behavior of the nonlinear excitation of magnons in ferromagnets. Both the long-range magnetic dipole-dipole and short-range exchange interactions are included, along with a static longitudinal applied field and a microwave pumping field in the perpendicular orientation. Within a microscopic (or Hamiltonian-based) approach the total Hamiltonian is transformed from spin operators to a normal-mode set of boson creation and annihilation operators. When the three-magnon interactions are included, it is found that the microwave pumping field may be used to control the nonlinear statistical properties of the system. From a study of the time evolution of the system we deduce the average number of magnons, the super-Poissonian statistical behavior, and the occurrence of magnon squeezing. We also compare the results with the case where the microwave pumping field is in the parallel orientation, and it is found that there are important differences in the time dependence.
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