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.

Accepted for publication in the Phil. Trans. R. Soc. A

References in corpus (4)

• Chaotic Dynamics of Spin-Valve Oscillators
• Switching of the vortex polarity in a magnetic nanodisk by a DC current
• 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

Cited by in corpus (57)

• Superdiffusion in spin chains
• Spin Dynamics in van der Waals Magnetic Systems
• Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
• Quantum Brownian Motion for Magnets
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• Uncovering footprints of dipolar-octupolar quantum spin ice from neutron scattering signatures
• Microscopic Theory of Ultrafast Skyrmion Excitation by Light
• Floquet resonances close to the adiabatic limit and the effect of dissipation
• Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions
• Exceptional points as signatures of dynamical magnetic phase transitions
• Bifurcation structure and chaos in nanomagnet coupled to Josephson junction
• Magnetic vortex liquid and anomalous thermal Hall conductivity in frustrated magnets with bond-dependent interactions
• Spin-transfer-driven nano-oscillators are equivalent to parametric resonators
• Skyrmion-Excited Spin Wave Fractal Network
• Generalization of group-theoretic coherent states for variational calculations
• Enhanced synchronization in an array of spin torque nano oscillators in the presence of oscillating external magnetic field
• From the open Heisenberg model to the Landau-Lifshitz equation
• Chirotactic response of microswimmers in fluids with odd viscosity
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• 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
• Intrinsic topological magnons in arrays of magnetic dipoles
• Controllable magnetic states in chains of coupled phi-0 Josephson junctions with ferromagnetic weak links
• Recent results for the Landau-Lifshitz equation
• The fractional Landau-Lifshitz-Gilbert equation
• Anisotropy-assisted magnon condensation in ferromagnetic thin films
• Multitude of exceptional points in van der Waals magnets
• 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
• Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque
• Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Magnonics in collinear magnetic insulating systems
• Effect of interfacial spin mixing conductance on gyromagnetic ratio of Gd substituted Y${}_3$Fe${}_5$O${}_{12}$
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Interplay between Exchange Interaction and Magnetic Shape Anisotropy of ferromagnetic nanoparticles in a non-magnetic matrix for rare-earth-free permanent magnets
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Quantum harvester enables energy transfer without randomness transfer or dissipation
• Floquet theory and applications in open quantum and classical systems
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• 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
• 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
• Breather bound states in a parametrically driven magnetic wire
• Nonequilibrium thermal state of a voltage-biased Mott insulator
• Hysteresis in magnets
• Spin Torque Oscillations Triggered by In-plane Field
• Discretization error analysis for a radially symmetric harmonic map heat flow problem
• Hamiltonian dynamics of classical spins
• Topological edge states in dipolar zig-zag stripes
• Magpy: A C++ accelerated Python package for simulating magnetic nanoparticle stochastic dynamics
• Computational Frameworks for Patterned Two-Dimensional Magnetism
• Unquenched orbital angular momentum as the origin of spin inertia
• Soliton-like behaviour in non-integrable systems
• Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra