Theory of spin-transfer torque and domain wall motion in magnetic nanostructures

This chapter develops the theory for the dynamics of domain walls in the context of spin electronic devices. The transfer of angular momentum (torque transfer) between an electrical current and a magnetic domain is discussed in the context of the Landau-Lifshitz equations and different relaxation models. In the context of these equations the transfer is reflected by a finite divergence of the spin current. In this context the Stoner and local moment models of ferromagnets are introduced. The Landau-Lifshitz description involves the classical magnetization and such a description implies a coupling to the environment which continually 'measures' the system. The experimental consequences of this are elaborated. The essential role of a 'spin motive force' in connection with conservation of energy is explained, and some device applications are outlined. The Lagrangian description of the dynamical modes of spin valves and domain walls is developed.