Landau–Lifshitz–Gilbert equation
Description of the dynamics of magnetization in a solid / From Wikipedia, the free encyclopedia
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In physics, the Landau–Lifshitz–Gilbert equation (usually abbreviated as LLG equation), named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the dynamics (typically the precessional motion) of magnetization M in a solid. It is a modified version by Gilbert of the original equation of Landau and Lifshitz.[1] The LLG equation is similar to the Bloch equation, but they differ in the form of the damping term. The LLG equation describes a more general scenario of magnetization dynamics beyond the simple Larmor precession. In particular, the effective field driving the precessional motion of M is not restricted to real magnetic fields; it incorporates a wide range of mechanisms including magnetic anisotropy, exchange interaction, and so on.
The various forms of the LLG equation are commonly used in micromagnetics to model the effects of a magnetic field and other magnetic interactions on ferromagnetic materials. It provides a practical way to model the time-domain behavior of magnetic elements. Recent developments generalizes the LLG equation to include the influence of spin-polarized currents in the form of spin-transfer torque.[2]