Our study delves into the dynamic and static spin structure factors of the α-T3 lattice, employing the Green's function approach, within the framework of the Kane–Mele and Hubbard model Hamiltonian. The dynamical spin susceptibility is directly related to the inelastic cross-section of the neutron beam interacting with the layer. Within this framework, analysis of the α-T3 lattice's spin excitation modes necessitates a thorough examination of the effect of the magnetic field, on-site Coulomb repulsion strength, and the spin-orbit coupling (SOC) parameter. This investigation is carried out by calculating the correlation function of the transverse components of spin density operators. Our findings reveal intriguing trends: The intensity of peaks in the inelastic cross-section varies with changes in on-site Coulomb repulsion. Moreover, our temperature-dependent assessment of the static spin structure factor indicates the manifestation of ferromagnetic behavior in the α-T3 lattice when α equals 0.5. Furthermore, the combined influence of SOC and magnetic fields amplifies the magnetic long-range order within the α-T3 lattice. The ability to manipulate the static spin structure factor and the imaginary dynamical transverse spin susceptibility holds promise across diverse domains, spanning from magnetic storage and spintronics to quantum computing and medical imaging.
