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

在磁开关器件的设计中，必须根据外场的形式、样品的几何形状和内部材料参数（包括表征自旋动力学阻尼的参数）来优化磁化反转过程。这种阻尼通常用自旋运动方程中的吉尔伯特阻尼项来描述，它只包含一个标量参数，即阻尼常数。到目前为止，所有的努力都是为了优化这个参数，假设它与磁态无关。对于具有大各向异性的系统，通常假设该参数很大，并且对于所有长度尺度（由微磁模拟中的细胞大小或仪器分辨率定义）使用该参数的一个唯一值就足够了。在本项目中，我们想研究吉尔伯特方程的局限性并探索其可能的必要扩展，我们想用从头算密度泛函电子理论计算与阻尼有关的材料参数。因此，我们使用了一个物理模型，它在绝热近似中包含了所有可能的阻尼贡献，并且在其最简单的形式中只包含一个参数。这使我们能够定量地计算吉尔伯特方程中各种可能的附加项的相对重要性。考虑具有不同维数和不同磁各向异性的系统，我们想研究阻尼和磁各向异性之间的关系。最后，我们将考虑描述不同长度尺度的阻尼参数的标度行为。

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.