Magnetization Dynamics in Ultrahigh-Density Magnetic Recording

Thermally activated magnetization reversal is a key consideration in the development of magnetic recording materials with ultrahigh densities. We consider the onset of magnetization reversal (nucleation) and describe the magnetization by a Langevin model, where the magnetization dynamics is realized by random thermal forces. The exchange, anisotropy, and Zeeman energies are expanded into powers of a small perpendicular magnetization component, and the dynamics reduces to a time-dependent superposition of normal modes. In the Stoner-Wohlfarth (SW) model, the approach reproduces the Arrhenius-N\'{e}el-Brown law $\tau$ = $\tau$$_{o}$ exp(E$_{a} $$\backslash$k$_{B}$T) with an approximate energy barrier E$_ {a} $ and a particle-size dependent constant $\tau$$_{o}$. The same is true for the micromagnetic approach, where the local micromagnetic parameters such as K$_{1}$(\textbf{r}) = $<$K$_{1} $(\textbf{r})$>$ give rise to nonuniform magnetization modes in inhomogeneous and interacting particles. However, both the coercivity H$_{c}$ and the energy barrier E$_{a}$ are smaller than the SW predictions. A further reduction of H$_{c}$ and E$_ {a}$ is obtained by taking into account local anisotropy fluctuations of the type $<$K$_{1}$(\textbf{r})$^{2}$$>$ - K$_ {1}$(\textbf{r})$^{2}$. This reduction corresponds to fluctuating energy barriers, and establishes a particle-shape and materials-dependent upper limit to energy barriers in very small particles.