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The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describemagnetization dynamics. We develop a unified framework of the microscopic LLGequation based on the nonequilibrium Green's function formalism. We present aunified treatment for expressing the microscopic LLG equation in severallimiting cases, including the adiabatic, inertial, and nonadiabatic limits withrespect to the precession frequency for a magnetization with fixed magnitude,as well as the spatial adiabatic limit for the magnetization with slowvariation in both its magnitude and direction. The coefficients of those termsin the microscopic LLG equation are explicitly expressed in terms ofnonequilibrium Green's functions. As a concrete example, this microscopictheory is applied to simulate the dynamics of a magnetic Skyrmion driven byquantum parametric pumping. Our work provides a practical formalism of themicroscopic LLG equation for exploring magnetization dynamics.

Unified framework of the microscopic Landau-Lifshitz-Gilbert equation and its application to Skyrmion dynamics