Spin structure factors of doped monolayer Germanene in the presence of spin-orbit coupling

TL;DR

This study investigates how spin-orbit coupling, magnetic fields, and doping influence the spin susceptibilities and dynamical spin structure factors of doped monolayer Germanene using a Kane-Mele model and Green's function approach.

Contribution

It introduces a comprehensive analysis of spin susceptibilities in doped Germanene considering spin-orbit coupling, magnetic fields, and temperature effects, extending previous models.

Findings

Spin-orbit coupling shifts magnetic excitation modes to higher frequencies.

Magnetic field affects the transverse susceptibility peaks, moving them to lower frequencies.

Doping and temperature significantly influence the static and dynamical spin responses.

Abstract

In this paper, we present a Kane-Mele model in the presence of magnetic field and next nearest neighbors hopping amplitudes for investigations of the spin susceptibilities of Germanene layer. Green's function approach has been implemented to find the behavior of dynamical spin susceptibilities of Germanene layer within linear response theoryand in the presence of magnetic field and spin-orbit coupling at finite temperature. Our results show the magnetic excitation mode for both longitudinal and transverse components of spin tends to higher frequencies with spin-orbit coupling strength. Moreover the frequency positions of sharp peaks in longitudinal dynamical spin susceptibility are not affected by variation of magnetic field while the peaks in transverse dynamical susceptibility moves to lower frequencies with magnetic field. The effects of electron doping on frequency behaviors of spin susceptibilities have been addressed in details. Finally the temperature dependence of static spin structure factors due to the effects of spin-orbit coupling, magnetic field and chemical potential has been studied.