Discovery and regulation of chiral magnetic solitons: Exact solution from Landau-Lifshitz-Gilbert equation

TL;DR

This paper introduces an exact solution approach for the nonlinear Landau-Lifshitz-Gilbert equation, revealing chiral magnetic solitons and enabling precise control in magnetic memory devices.

Contribution

It establishes a novel geometric mapping linking the LLG equation to an integrable nonlinear Schrödinger equation, allowing for exact solutions of complex magnetic phenomena.

Findings

Discovery of exact chiral magnetic solitons.

Mapping enables solving the nonlinear LLG equation.

Facilitates control of magnetic states via spin current injection.

Abstract

The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and indispensable framework within the realm of magnetism. However, solving the LLG equation, encompassing full nonlinearity amidst intricate complexities, presents formidable challenges. In this context, we develop a precise mapping through geometric representation, establishing a direct linkage between the LLG equation and an integrable generalized nonlinear Schr\"odinger equation. This novel mapping provides accessibility towards acquiring a great number of exact spatiotemporal solutions. Notably, exact chiral magnetic solitons, critical for stability and controllability in propagation with and without damping effects are discovered. Our formulation provides exact solutions for the long-standing fully nonlinear problem, facilitating practical control through spin current injection in magnetic memory applications.