Magnetization direction-controlled topological band structure in TlTiX (X = Si, Ge) monolayers.

The quantum anomalous Hall (QAH) insulator is a vital material for the investigation of emerging topological quantum effects, but its extremely low working temperature limits experiments. Apart from the temperature challenge, effective regulation of the topological state of QAH insulators is another crucial concern. Here, by first-principles calculations, we find a family of stable two-dimensional materials TlTiX (X = Si, Ge) are large-gap QAH insulators. Their extremely robust ferromagnetic (FM) ground states are determined by both the direct- and super-exchange FM coupling. In the absence of spin-orbit coupling (SOC), there exist a spin-polarized crossing point located at eachand' points, respectively. The SOC effect results in the spontaneous breaking ofsymmetry and introduces a mass term, giving rise to a QAH state with sizable band gap. The tiny magnetocrystalline anisotropic energy (MAE) implies that an external magnetic field can be easily used to align magnetization deviating fromdirection to the-plane, thereby leading to a transformation of the electronic state from the QAH state to the Weyl half semimetals state, which indicate monolayers TlTiX (X = Si, Ge) exhibit a giant magneto topological band effect. Finally, we examined the impact of stress on the band gap and MAE, which underlies the reasons for the giant magneto topological band effect attributed to the crystal field. These findings present novel prospects for the realization of large-gap QAH states with the characteristic of easily modifiable topological states.