2.2
Landau-Lifshitz-Gilbert Equation
The equation that governs the dynamics of magnetization distribution in a magnetic material is due to Lev Landau, and Evgeny Lifshitz and T. L. Gilbert and is called LandauLifshitz-Gilbert (LLG) equation. ∂ αγ M(r, t) = −γM(r, t) × Heff (r, t) − M(r, t) × M(r, t) × Heff (r, t) ∂t Ms
(2.1)
Here γ is the electron gyromagnetic ratio, α is the damping constant and Heff is the effective magnetic field acting on the magnetization. The effect of LLG equation is to align or anti-align the magnetization vector with the effective field by going through a precession motion as shown in Fig. 2.2.
H eff M (M H eff )
M t M H eff
M
Figure 2.2: Landau-Lifshitz-Gilbert Equation.
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