We consider spin dynamics for implementation in an atomistic framework and weaddress the feasibility of capturing processes in the femtosecond regime byinclusion of moment of inertia. In the spirit of an {\it s-d} -like interactionbetween the magnetization and electron spin, we derive a generalized equationof motion for the magnetization dynamics in the semi-classical limit, which isnon-local in both space and time. Using this result we retain a generalizedLandau-Lifshitz-Gilbert equation, also including the moment of inertia, anddemonstrate how the exchange interaction, damping, and moment of inertia, allcan be calculated from first principles.
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机译：我们考虑在原子框架中实现自旋动力学，并通过包含惯性矩来解决在飞秒状态下捕获过程的可行性。本着磁化和电子自旋之间类似{\ s s-d}相互作用的精神，我们推导了半经典极限中磁化动力学的广义运动方程，该方程在空间和时间上都是非局部的。使用该结果，我们保留了一个广义的Landau-Lifshitz-Gilbert方程，其中也包括惯性矩，并演示了如何根据第一原理来计算交换相互作用，阻尼和惯性矩。
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