The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview

Abstract

The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well known integrable soliton equations, including nonlinear Schrödinger and sine-Gordon equations. It can admit very many dynamical structures including spin waves, elliptic function waves, solitons, dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the physical and spin dimensions and the nature of interactions. An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation which forms a basic dynamical equation in the field of spintronics. This article will briefly review these developments as a tribute to Robin Bullough who was a great admirer of the LLG equation.

arXiv commentAccepted for publication in the Phil. Trans. R. Soc. A

References in corpus (11)

• Synchronization of spin-transfer oscillators driven by stimulated microwave currents
• Current Induced Magnetization Switching in Small Domains of Different Anisotropies
• Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions
• Chaotic Dynamics of Spin-Valve Oscillators
• Switching of the vortex polarity in a magnetic nanodisk by a DC current
• Discrete breathers in classical spin lattices
• Spin-transfer torque induced reversal in magnetic domains
• Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field
• Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis
• Dynamic and Static Excitations of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
• Equatorial and related non-equilibrium states in magnetization dynamics of ferromagnets: Generalization of Suhl's spin-wave instabilities

Cited by in corpus (101)

• Recent Advances in Physical Reservoir Computing: A Review
• Unconventional magnetism via optical pumping of interacting spin systems
• Superdiffusion in spin chains
• Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
• Skyrmion-Antiskyrmion pair creation by in-plane currents
• Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
• Spin Dynamics in van der Waals Magnetic Systems
• Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
• Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
• Quantum Brownian Motion for Magnets
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• Comparison of quantum and classical relaxation in spin dynamics
• Uncovering footprints of dipolar-octupolar quantum spin ice from neutron scattering signatures
• Symplectic integrators for spin systems
• Topological dynamics and current-induced motion in a skyrmion lattice
• Intrinsic Localized Modes of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
• The magnetic monopole and the separation between fast and slow magnetic degrees of freedom
• Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques
• Microscopic Theory of Ultrafast Skyrmion Excitation by Light
• A minimal-variable symplectic integrator on spheres
• Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets
• Floquet resonances close to the adiabatic limit and the effect of dissipation
• Darboux Transformation and Exact Solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
• Synchronization of an array of spin torque nano oscillators in periodic applied external magnetic field
• Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions
• On the Relationship between the One-Corner Problem and the $M$-Corner Problem for the Vortex Filament Equation
• Solitons in a continuous classical Haldane-Shastry spin chain
• Exceptional points as signatures of dynamical magnetic phase transitions
• Bifurcation structure and chaos in nanomagnet coupled to Josephson junction
• Terahertz spin dynamics driven by a field-derivative torque
• Magnetic vortex liquid and anomalous thermal Hall conductivity in frustrated magnets with bond-dependent interactions
• Skyrmion-Excited Spin Wave Fractal Network
• Spin-transfer-driven nano-oscillators are equivalent to parametric resonators
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• Chirotactic response of microswimmers in fluids with odd viscosity
• From the open Heisenberg model to the Landau-Lifshitz equation
• Enhanced synchronization in an array of spin torque nano oscillators in the presence of oscillating external magnetic field
• Generalization of group-theoretic coherent states for variational calculations
• Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation
• Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Multiscale thermodynamics of charged mixtures
• Intrinsic topological magnons in arrays of magnetic dipoles
• Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality
• Voltage Control of Magnetic Monopoles in Artificial Spin Ice
• Rashba induced chirality switching of domain walls and suppression of the Walker breakdown
• Anisotropy-assisted magnon condensation in ferromagnetic thin films
• Recent results for the Landau-Lifshitz equation
• The fractional Landau-Lifshitz-Gilbert equation
• An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
• Controllable magnetic states in chains of coupled phi-0 Josephson junctions with ferromagnetic weak links
• Integrable motion of two interacting curves, spin systems and the Manakov system
• Phase locking of spin transfer nano-oscillators using common microwave sources
• Exact Intrinsic Localized Excitation of an Anisotropic Ferromagnetic Spin Chain in External Magnetic Field with Gilbert Damping, Spin Current and PT-Symmetry
• Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping
• Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder
• Multitude of exceptional points in van der Waals magnets
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque
• Magnonics in collinear magnetic insulating systems
• Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation
• Spin Dynamics in Driven Composite Multiferroics
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Impact of the crystal orientation on spin-orbit torques in Fe/Pd bilayers
• Effect of interfacial spin mixing conductance on gyromagnetic ratio of Gd substituted Y${}_3$Fe${}_5$O${}_{12}$
• Electron g-factor engineering for non-reciprocal spin photonics
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Interplay between Exchange Interaction and Magnetic Shape Anisotropy of ferromagnetic nanoparticles in a non-magnetic matrix for rare-earth-free permanent magnets
• Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations
• Inhomogeneous domain walls in spintronic nanowires
• Floquet theory and applications in open quantum and classical systems
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Quantum harvester enables energy transfer without randomness transfer or dissipation
• Dynamic Spin-Lattice Coupling and Statistical Interpretation for the Molecular-Like Excitations in Frustrated Pyrochlores
• Ultrafast dynamics of a spin-polarized electron plasma with magnetic ions
• Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents
• Dynamic Response in a Finite Size Composite Multiferroic Thin Film
• Spin-transfer torque driven localized spin excitations in the presence of field-like torque
• Tailoring the topological details of the magnetic skyrmion by the spin configuration at the edges
• Stochastic Thermodynamics of oscillators networks
• Poissonization of Three Dimensional Nonholonomic Dynamics with the Method of Extension
• Breather bound states in a parametrically driven magnetic wire
• Relaxation to equilibrium in models of classical spins with long-range interactions
• Nonequilibrium thermal state of a voltage-biased Mott insulator
• Towers with skeletons for the (2+1)-dimensional continuous isotropic Heisenberg spin model
• A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian
• Spin Torque Oscillations Triggered by In-plane Field
• Discretization error analysis for a radially symmetric harmonic map heat flow problem
• The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
• Topological edge states in dipolar zig-zag stripes
• Landau-Lifshitz Equation with Affine Control
• SU(2s+1) symmetry and nonlinear dynamic equations of spin s magnets
• Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra
• Unquenched orbital angular momentum as the origin of spin inertia
• Magpy: A C++ accelerated Python package for simulating magnetic nanoparticle stochastic dynamics
• Hysteresis in magnets
• Computational Frameworks for Patterned Two-Dimensional Magnetism
• Soliton-like behaviour in non-integrable systems
• Hamiltonian dynamics of classical spins