Pinning effect on current-induced magnetic transverse domain wall dynamics in nanostrip is studied for its potential application to new magnetic memory devices. In this study, we carry out a series of calculations by solving generalized Landau-Lifshitz equation involving a current spin transfer torque in one and two dimensional models. The critical current for the transverse wall depinning in nanostrip depends on the size of artificial rectangular defects on the edges of nanostrip. We show that there is intrinsic pinning potential for a defect such that the transverse wall oscillates damply around the pinning site with an intrinsic frequency if the applied current is below critical value. The amplification of the transverse wall oscillation for both displacement and maximum value of m3 is significant by applying AC current and current pulses with appropriate frequency. We show that for given pinning potential, the oscillation amplitude as a function of the frequency of the AC current behaves like a Gaussian distribution in our numerical study, which is helpful to reduce strength of current to drive the transverse wall motion.

We study the homogenization process of ferromagnetic multilayers in the presence of surface energies:super-exchange, also called interlayer exchange coupling,and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequenceof extension operators for the multilayer geometry.First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is inversely proportional to the interlayer distance. We establishthe homogenized equation in these two situations.

In this article, we prove the existence and uniqueness of solution for the Cauchy problem of the Landau-Lifshitz equation of ferromagnetism with external magnetic field. We also show that the solution is globally regular with the exception of at most finitely many blow-up points. An energy identity at blow-up points is presented.