Dynamical spin susceptibility and magnetic ordering in a square-octagon lattice in the Hubbard model

In this work, we investigate the electronic and magnetic properties of the two-dimensional square-octagon structure (2DSOS) using a tight-binding framework augmented by on-site Coulomb interaction. We examine how varying hopping parameters, magnetic flux, and interaction strength influence the system's band structure, dynamical transverse spin susceptibility (DTSS), and static spin structure factor (SSSF). Our findings reveal the emergence of a flat band when the third-nearest-neighbor hopping term t₃ equals the nearest-neighbor hopping t₁, significantly affecting the magnetic response. The frequency dependence of the DTSS demonstrates that both magnetic flux and Coulomb repulsion shift the resonance peaks to higher frequencies and suppress their intensities, indicating a suppression of low-energy spin fluctuations. Moreover, the temperature dependence of the SSSF underlines a transition from paramagnetic to ferromagnetic behavior as the ratio t₂/t₁ increases. These results highlight the crucial role of electronic correlations and lattice geometry in shaping the spin dynamics of flat-band systems and offer valuable insights for designing future spintronic and correlated electron devices.