Calculating the Mognons Energy in Ferromagnetic Materill with spin S=1/2 in Complex Coordinate System

This research aimes to studasome nonlinear phynomenons wich, noticed in magnetic systems (ferromagnetic material) that produced from primer dicturbance of moments, that erranged in parallel and in the same direction, because they affected by externol factor (magnetic field , which has constant intensity and variable direction or variable intensity and constant direction or thermol effect ) that seemed in waves form propecate in crystal and called spin waves (magnons).