The fractional Landau-Lifshitz-Gilbert equation

Abstract

The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order $s\ge 0$. We show that the parameter $s$ can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.

28 (6 manuscript + 22 supplementary) pages, 3 (2 manuscript + 1 supplementary) figures

References in corpus (3)

• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Functional Keldysh Theory of Spin Torques
• Geometric Quantum Noise of Spin

Cited by in corpus (6)

• Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
• Bath-induced spin inertia
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Dissipative systems fractionally coupled to a bath
• Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra
• Optically induced magnetic inertia and magnons from non-Markovian extension of the Landau-Lifshitz-Gilbert equation