Magnetization Direction

Figure 7.8. Sketch of double-well potential showing the energy plotted against the orientation of the magnetization for up and down orientations of magnetic nanoparticles in the absence

(-•) and presence (----) of an applied magnetic field. [With permission from

D. D. Awschalom arid D. P. DiVincenzo, Phys. Today 44 (April 1995).]

thermal activation, due to an Arrhenius process, where the probability P for reorientation is given by where E is the height of the energy barrier between the two orientations. The particle can also flip its orientation by a much lower probability process called quantum-mechanical tunneling. This can occur when the thermal energy kB T of the particle is much less than the barrier height. This process is a purely quantum-mechanical effect resulting from the fact that solution to the wave equation for this system predicts a small probability for the up state of the magnetization to change to die down state. If a magnetic field is applied, the shape of die potential changes, as shown by the dashed line in Fig. 7.8, and one minimum becomes unstable at the coercive field

The SW model provides a simple explanation for many of the magnetic properties of small magnetic particles, such as the shape of die hysteresis loop. However, the model has some limitations. It overestimates the strength of the coercive field because it allows only one path for reorientation. The model assumes that die magnetic energy of a particle is a function of the collective orientation of die spins of the magnetic atoms in die particle and the effect of the applied DC magnetic field. This implies that the magnetic energy of the particle depends on its volume. However, when particles are in the order of 6 nm in size, most of their atoms are

on the surface, which means that they can have very different magnetic properties than larger grain particles. It has been shown that treating the surfaces of nanoparticles of o-Fe that are 600 nm long and lOOnm wide with various chemicals can produce variations in the coercive field by as much as 50%, underlining the importance of the surface of nanomagnetic particles in determining the magnetic properties of the grain. Thus the dynamical behavior of very small magnetic particles is somewhat more complicated than predicted by the SW model, and remains a subject of continuing research.

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