- Landau–Lifshitz–Gilbert equation
In physics, the Landau-Lifshitz-Gilbert equation , named for Lev Landau and Evgeny Lifshitz and T. L. Gilbert, is a name used for a differential equation describing the precessional motion of magnetization M in a solid. It is a modification by Gilbert of the original equation of Landau and Lifshitz.
Landau-Lifshitz ordinary differential equation
The LLE introduced by harvtxt|Landau|Lifshitz|1935 to model the precessional motion of magnetization M in a solid with an effective magnetic field H and with damping. It is the ordinary differential equation:The constants α is the Landau-Lifshitz phenomenological damping parameter and depends on the solid, and γ is the electron gyromagnetic ratio.
The LLE above works fairly well when the damping is small, but fails for large damping. To fix this problem harvtxt|Gilbert|1955 suggested a different damping term.The resulting equation is called the Landau-Lifshitz-Gilbert equation, and is given by:where α is called the Gilbert damping constant. Any solution also satisfies the Landau-Lifshitz equation for γ replaced by γ/(1+α2).
* [http://www.bama.ua.edu/~tmewes/Java/dynamics/MagnetizationDynamics.shtml Magnetization dynamics applet]
*citation|first=T.L.|last= Gilbert|title=A Lagrangian formulation of the gyromagnetic equation of the magnetic field|journal= Physical Review|volume= 100 |year=1955|page= 1243 This is only an abstract; the full report is "Armor Research Foundation Project No. A059, Supplementary Report, May 1, 1956", but was never published. A description of the work is given in citation|first=T. L.|last= Gilbert|journal = IEEE Trans. Mag.
doi=10.1109/TMAG.2004.836740|title=A phenomenological theory of damping in ferromagnetic materials
*citation|authorlink1=Lev Landau|authorlink2=Evgeny Lifshitz|first=L.D. |last=Landau|first2= E.M.|last2= Lifshitz|title= Theory of the dispersion of magnetic permeability in ferromagnetic bodies|journal= Phys. Z. Sowietunion|volume= 8, 153 |year=1935
*citation|title=The Landau-Lifshitz equation revisited
first=G V|last= Skrotskiĭ |year=1984 |journal=Sov. Phys. Usp.|volume= 27 |pages=977-979 |doi=10.1070/PU1984v027n12ABEH004101
title=Landau-Lifshitz Equations |series=Frontiers of Research With the Chinese Academy of Sciences
first=Boling |last=Guo |first2= Shijin |last2=Ding|year=2008
publisher=World Scientific Publishing Company
Look at other dictionaries:
Landau–Lifshitz equation — In physics, the Landau Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a name used for several different differential equations *For the Landau Lifshitz aeroacoustic equation see aeroacoustics. *For the Landau Lifshitz… … Wikipedia
Lev Landau — Infobox Scientist name = Lev Davidovich Landau imagesize = 170px birth date = birth date|1908|1|22|mf=y birth place = Baku, Russian Empire death date = death date and age|1968|4|1|1908|1|22 death place = Moscow, Soviet Union field = Physics alma… … Wikipedia
Micromagnetics — deals with the interactions between magnetic moments on sub micrometre length scales. These are governed by several competing energy terms. Dipolar energy is the energy which causes magnets to align north to south pole. Exchange energy will… … Wikipedia
Magnetization dynamics — Contents 1 Rotation Physics 2 Precession 3 Damping 4 Landau Lifshitz Gilbert Equation 5 References … Wikipedia
Magnonics — is an emerging field of modern magnetism, which can be considered a sub field of modern solid state physics. Magnonics combines waves and magnetism, its main aim is to investigate the behaviour of spin waves in nano structure elements. In… … Wikipedia
Micromagnetism — General= Micromagnetism deals with the interactions between magnetic moments on sub micrometre length scales. These are governed by several competing energy terms. Dipolar energy is the energy which causes magnets to align north to south pole.… … Wikipedia
List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… … Wikipedia
Magnetic moment — Electromagnetism Electricity · … Wikipedia
Spin wave — Spin waves are propagating disturbances in the ordering of magnetic materials. These low lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as… … Wikipedia
Magnon — Les magnons sont des modes d excitation ou ondes de spin. Dans un milieu ferromagnétique isotrope en dessous de la température de Curie, ou dans un milieu antiferromagnétique en dessous de la température de Néel, les moments magnétiques des… … Wikipédia en Français