Analytical solutions for ultra-fast precessional switching in inertial magnetization dynamics

TL;DR

This paper derives analytical solutions for ultra-fast magnetization switching in ferromagnetic nanoparticles, incorporating inertial effects, and validates these solutions through numerical simulations, aiming to improve energy-efficient memory technologies.

Contribution

It introduces a perturbation-based analytical approach to model inertial effects in ultra-fast magnetization switching, providing explicit formulas for switching time and safety margins.

Findings

Analytical formulas accurately predict switching dynamics.

Inertial effects significantly influence switching times.

Validation confirms the model's applicability to real systems.

Abstract

Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast magnetization dynamics that may eventually end up in the reversed equilibrium realizing successful precessional switching. We consider ultra-short pulse duration (fractions of picosecond) and large external field intensities (several Tesla) which may be relevant for the realization of faster energy-efficient memory cells. For such short time scales, we include inertial effects in the theoretical description by considering the inertial Landau-Lifshitz-Gilbert equation which requires to be treated as a system of singularly perturbed ODEs for small values of the inertia. By using suitable perturbation approach based on multiple time scales analysis, we develop an approximate closed-form solution for the switching dynamics as well as formulas for switching time and its safety tolerances to obtain the successful switching as function of physical parameters of the particle and strength of magnetic inertia. The developed analytical solution is validated by numerical simulations.