固有吉尔伯特阻尼的起源
Origin of intrinsic Gilbert damping
摘要：
磁化的阻尼，由它松弛到平衡的速率表示，被成功地建模为Landau-Lifschitz-Gilbert方程的唯象扩展。这是称为吉尔伯特阻尼的阻尼转矩项，其方向由磁化强度及其时间导数的矢量积给出。在这里，我们从第一原理通过狄拉克方程的非相对论展开推导出吉尔伯特项。我们发现，吉尔伯特项出现时，一个计算的时间演化的自旋可观察的存在下的完整的自旋-轨道耦合项，同时认识到之间的关系的旋度的电场和随时间变化的磁感应强度。
英文摘要：
The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.
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