Contents

Section 1. Metodological notes

Introduction to Ferromagnetic Spintronics: Pedagogical Notes

A.V. Rozhkov

Abstract

The article presents foundational theoretical material that lays the groundwork for understanding modern scientific research in the field of spintronics. The following topics are analyzed: the Landau–Lifshitz equation, spin diffusion processes in non-magnetic metals, and the interaction of charge carrier spins with the magnetization of a conducting ferromagnet through the inclusion of the so-called transferred spin torque. The adiabatic approximation is discussed in detail. It provides a clear picture of how an electric current flowing through a ferromagnetic conductor generates an additional torque due to the necessity of changing the carrier spins’ polarization direction, which aligns parallel to the local ferromagnetic magnetization. Accounting for corrections to the adiabatic approximation requires incorporating dissipative processes in the electron spin subsystem into the model. Dissipation introduces additional and qualitatively new contributions to the dynamic equation for the magnetization of the ferromagnet. In this work, we present two types of solutions to the resulting evolution equation. In particular, it will be shown that a current flowing through the system destabilizes the uniform state, provided, of course, that the current is sufficiently strong. The main goal of these pedagogical notes is to present the derivation of a generalized Landau–Lifshitz equation that accounts for the influence of carrier spins on the dynamics of ferromagnetic magnetization, as well as to analyze the features of the theoretical formalism and the approximations made.

Keywords: spintronics, Landau-Lifshits equation, spin-transfer torque, spin relaxation, homogeneous state instability