Landau–Lifshitz–Gilbert equation

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. 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.