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Magnetization dynamics in magnetic materials are well described by themodified semiclassical Landau-Lifshitz-Gilbert (LLG) equation, which includesthe magnetic damping $\alpha$ and the magnetic moment of inertia $\mathrm{I}$tensors as key parameters. Both parameters are material-specific and physicallyrepresent the time scales of damping of precession and nutation inmagnetization dynamics. $\alpha$ and $\mathrm{I}$ can be calculated quantummechanically within the framework of the torque-torque correlation model. Thequantities required for the calculation are torque matrix elements, the realand imaginary parts of the Green's function and its derivatives. Here, wecalculate these parameters for the elemental magnets such as Fe, Co and Ni inan ab initio framework using density functional theory and Wannier functions.We also propose a method to calculate the torque matrix elements within theWannier framework. We demonstrate the effectiveness of the method by comparingit with the experiments and the previous ab initio and empirical studies andshow its potential to improve our understanding of spin dynamics and tofacilitate the design of spintronic devices.

Calculation of Gilbert damping and magnetic moment of inertia using torque-torque correlation model within ab initio Wannier framework