## Magnetization Dynamics

The precise understanding of switching processes of nano-magnets is important for magnetic heads, sensors, and spin electronics applications. Since the speed of the data read-write process is increasing, the calculation of the high-speed switching in magnetic recording media is currently becoming a matter of considerable importance, because of the potential limitation on data rates that this phenomena produces.

The theoretical treatment of the magnetization dynamics at zero temperature starts from the integration of the Landau-Lifshitz-Gilbert equation [112, 120]

where y is the gyromagnetic factor, a is the damping parameter, Ms is the saturation magnetization value, and Hf = -8E/8M is the total effective field, which includes external field, anisotropy, exchange, and magnetostatic contributions. This equation contains a term describing the precession of the magnetic moment around the internal field direction and a phenomenological damping term. Since the period of the precessional motion of a magnetic moment is of the order of 10-11 s, the total elapsed time of these calculations is of the order of ns [120]. However, the potential applications related to this rate of the magnetization switching are rapidly approaching this scale. The dynamical calculations, even if used to calculate the magnetization minima do not always lead to the same micromagnetic structure due to the presence of the precession, which takes the system magnetization out of thin film plane and makes other magnetization minima accessible. For example, calculations in soft-hard nanocrystalline NdFeB-based permanent magnets have shown that the gyromagnetic precession of the magnetization reduces the coercive field by about 10% as compared to the coercive field obtained with static micro-magnetic calculations [158].

The precessional response and the magnetization damping govern the upper limit of the switching speed. One of the experimental characterizations of high speed switching is related to dynamic coercivity measurements in which the remanent magnetization and coercivity are measured as a function of the duration and intensity of the applied field pulse [160] (Fig. 19). The calculations related to this experimental procedure have shown that in a granular materials with noninteracting grains, the remanent magnetization curves as a function of the reverse peak duration are very sensitive to the value of the damping constant [122]. For

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