Magnetization nutation in magnetic semiconductors: Effective spin model with anisotropic RKKY exchange interaction

TL;DR

This paper investigates magnetization nutation in magnetic semiconductors caused by anisotropic RKKY exchange interactions, deriving an effective spin model that explains the underlying physics and potential for spintronic applications.

Contribution

It introduces an effective XXZ spin model with anisotropic exchange couplings derived from conduction electron band splitting in magnetic semiconductors.

Findings

Derived analytical formulas for anisotropic exchange interactions.

Showed magnetization exhibits nutational motion under external fields.

Linked conduction band splitting to effective spin dynamics.

Abstract

We demonstrate that the magnetization in magnetic semiconductors exhibits nutational motion when subjected to an external magnetic field. This behavior originates from the splitting of the conduction-electron band which induces anisotropic, distance-dependent exchange coupling between localized spins. To investigate this phenomenon, we examine a general system that includes both charge and spin degrees of freedom, characteristic of a magnetic semiconductor. This system is composed of two subsystems: (1) a gas of noninteracting conduction electrons and (2) a ferromagnetic array of localized spins, coupled through the Vonsovskii (\textit{sd}) local interaction. The entire system is subject to external electrical and magnetic disturbances. Through the Feynman-Schwinger formalism, we integrate out the faster (Grassmann) charge degrees of freedom associated with the conduction electrons to obtain the effective Hamiltonian for the localized spins in the form of an XXZ spin model. We then provide general analytical formulas for the corresponding anisotropic exchange couplings, expressed in Fourier and direct spaces, as functions of the effective field that induces conduction-band splitting. .... We hope this study will motivate further research into nutational phenomena in magnetic semiconductors, possibly resulting in improvements in the accurate control of magnetization dynamics within spin-based electronic devices.