Limitations and extensions of the Gilbert equation, and calculation of material parameters related to spin damping: An ab-initio study

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For the design of magnetic switching devices it is essential to optimize the magnetization reversal process with respect to the form of the external field, the geometry of the sample and the internal material parameters including those characterizing the damping of the spin dynamics. This damping is usually described by a Gilbert damping term in the equation of motion for the spins, which contains only one scalar parameter, the damping constant. All the efforts so far were devoted to optimize this parameter which is assumed to be independent of the magnetic state. It is often assumed that this parameter is large for systems with large anisotropy, and that it suffices to use one unique value of this parameter for all length scales (defined by the cell size in micromagnetic simulations, or by the instrumental resolution). In the present project we want to investigate the limitations of the Gilbert equation and to explore their possible necessary extensions, and we want to calculate the material parameters related to damping by the ab-initio density functional electron theory. Thereby we use a physical model which contains all possible contributions to damping in adiabatic approximation and which - in its simplest form - contains only one parameter. This enables us to calculate quantitatively the relative importance of various possible additional terms to the Gilbert equation. By considering systems with various dimensionality and hence various magnetic anisotropy we want to investigate the relation between damping and magnetic anisotropy. Finally, we will consider the scaling behaviour of the parameters describing damping for various length scales.