Abstract
This chapter analyzes large magnetization motions of precessional dynamics. In the case of applied magnetic fields, this dynamic is conservative, as magnetic free energy is conserved. The analysis of the geometric aspects of conservative precessional dynamics is revealed by its phase portrait, which is completely characterized by the energy extremal points—maxima, minima, saddles, and trajectories passing through saddles. These trajectories are called separatrices because they create a natural partition of the phase portrait into “central regions,” which may enclose energy minima, energy maxima, or separatrices. The “unit-disk” representation of the phase portrait of the precessional dynamics is also introduced. In this representation, cartesian axes coincide with the principal anisotropy axes, and it is assumed that at least one cartesian component of the applied magnetic field is equal to zero. These elliptic curves completely represent the phase portrait of the magnetization dynamics on the unit sphere and are important because they represent the separatrices of the magnetization dynamics.
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