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.
9-869: [REDACTED] Look up llg in Wiktionary, the free dictionary. LLG or variation , may refer to: The Landau–Lifshitz–Gilbert equation , used in micromagnetics Local government Local-level governments of Papua New Guinea The Logical Language Group Lole language (ISO 639 code: llg ) Lycée Louis-le-Grand , a well known public high school in Paris Chillagoe Airport , IATA airport code "LLG" See also [ edit ] [REDACTED] Search for "llg" on Misplaced Pages. All pages with titles beginning with LLG All pages with titles containing LLG 2LG LG (disambiguation) Topics referred to by
18-433: Is a dimensionless constant called the damping factor. The effective field H eff is a combination of the external magnetic field, the demagnetizing field , and various internal magnetic interactions involving quantum mechanical effects, which is typically defined as the functional derivative of the magnetic free energy with respect to the local magnetization M . To solve this equation, additional conditions for
27-505: Is different from Wikidata All article disambiguation pages All disambiguation pages Landau%E2%80%93Lifshitz%E2%80%93Gilbert equation 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
36-531: Is the dimensionless damping parameter, τ ⊥ {\displaystyle \tau _{\perp }} and τ ∥ {\displaystyle \tau _{\parallel }} are driving torques, and x is the unit vector along the polarization of the current. Demagnetizing field Too Many Requests If you report this error to the Wikimedia System Administrators, please include
45-556: The LL equation, the precessional term γ' depends on the damping term. This better represents the behavior of real ferromagnets when the damping is large. In 1996 John Slonczewski expanded the model to account for the spin-transfer torque , i.e. the torque induced upon the magnetization by spin -polarized current flowing through the ferromagnet. This is commonly written in terms of the unit moment defined by m = M / M S : where α {\displaystyle \alpha }
54-417: The LLG equation to include the influence of spin-polarized currents in the form of spin-transfer torque . In a ferromagnet , the magnitude of the magnetization M at each spacetime point is approximated by the saturation magnetization M s (although it can be smaller when averaged over a chunk of volume). The Landau-Lifshitz equation, a precursor of the LLG equation, phenomenologically describes
63-573: The demagnetizing field must be included to accommodate the geometry of the material. In 1955 Gilbert replaced the damping term in the Landau–Lifshitz (LL) equation by one that depends on the time derivative of the magnetization: This is the Landau–Lifshitz–Gilbert (LLG) equation, where η is the damping parameter, which is characteristic of the material. It can be transformed into the Landau–Lifshitz equation: where In this form of
72-457: The rotation of the magnetization in response to the effective field H eff which accounts for not only a real magnetic field but also internal magnetic interactions such as exchange and anisotropy. An earlier, but equivalent, equation (the Landau–Lifshitz equation) was introduced by Landau & Lifshitz (1935) : where γ is the electron gyromagnetic ratio and λ is a phenomenological damping parameter, often replaced by where α
81-403: The same term [REDACTED] This disambiguation page lists articles associated with the title LLG . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=LLG&oldid=1078747751 " Category : Disambiguation pages Hidden categories: Short description
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