On Ultrafast Spin Dynamics: Spin Dependent Fast Response of Hot Electrons, of Band--Structure

TL;DR

This paper investigates the ultrafast, spin-dependent responses of hot electrons in ferromagnetic materials, revealing how energy shifts and spin flip dynamics influence magnetic and electronic behaviors during non-equilibrium conditions.

Contribution

It introduces a theoretical analysis of spin-dependent energy shifts and response times of hot electrons, highlighting the impact of molecular fields on ultrafast spin dynamics in ferromagnetic systems.

Findings

Minority hot electrons respond faster than majority electrons.

Spin flip transitions are delayed by the molecular field.

Energy shifts depend on spin and non-equilibrium conditions.

Abstract

Different energy shifts for majority and minority electrons occur. Thus, for example in case of (laser) excited ferromagnetic metals majority and minority electrons may respond differently in time during closing the exchange splitting. Spin flip transitions of the hot electrons due to electron interactions cause quasi hybridization of the spin split states. This is also the case in itinerant ferromagnetic metals due to hopping between sites having magnetic moments pointing in direction of the magnetization (+) and opposite direction (-) and with energy levels $\varepsilon^+_{i\sigma}$ and $\varepsilon^-_{i\sigma}$. For energetic reasons the molecular field acts asymmetrically on the spins of the electrons and on spin flip transitions and thus causes different lifetimes of minority and majority electrons and spin dependent electron energy shifts. Quite general minority hot electrons in spin split states may respond faster than majority electrons at non--equilibrium. The molecular field acting on the spins delays spin flip transitions $\uparrow \rightarrow \downarrow$ and thus a response of the hot majority electrons and their energy levels. The closing of the exchange splitting in the electron spectrum of ferromagnetic transition and rare--earth metals, ferromagnetic semiconductors, spin split quantum well states in thin ferromagnetic films, etc. will reflect this. The time and spin dependent energy shifts of electrons at non--equilibrium may cause interesting behavior, in particular of magnetic tunnel junctions, spin currents etc.. In ferromagnets the moment reversal lifetime of (local) magnetic moments parallel to the global magnetization is larger than of moments pointing in opposite direction.