A controllable magneto-topological property and band gap engineering in 2D ferromagnetic Lieb lattice

In this paper, we study theoretically the magneto-topological property and gap engineering of two-dimensional ferromagnetic Lieb lattice by taking into account the next-nearest-neighbors (NNN) coupling and the important Dzyaloshinsky-Moriya interaction (DMI). In particular, the density of states and dispersion energy of the system in terms of various NNN and DMI in the presence of Zeeman field produce the main features in the context of Heisenberg model, Holstein-Primakoff transformation, and Green's function approach. It is found that the inclusion of NNN coupling opens a gap, leading to the metal-semiconductor-insulator transition depending on its intensity. Furthermore, DMI introduces two extra degenerate bands in the vicinity of Fermi-level due to the Stark effect. The magneto-topological property of the gap in our model is determined by the tunneling probability of particles at both weak and strong NNN and DMI regimes. Finally, we discuss the extension of nuclear spins to arbitrary values.