Spin-split flat bands at the band edge and two-dimensional hole gases towards quantum Hall effect in altermagnetic CoF$_2$

Abstract

Altermagnetic phase is recently found as a new magnetic phase in addition to the conventional collinear spin orders, and great efforts have been made to explore novel effects and potential applications in such materials. Here, we show that there are robust altermagnetic spin-split flat bands near the valence band edge in rutile CoF$_2$ through first-principles investigation. It is uncovered that the magnetic moments can remain in the z axis because of the magnetocrystalline energy due to the spin-orbits coupling and the spin orientation can be made more stable by magnetic field applied in the xy plane. We describe the spin-dependent band structure (including the flat bands) near the Fermi level by a spin-resolved effective low-energy model, and reveal that they can host spin-dependent two-dimensional hole gases. Importantly, we find spin-dependent quantum Hall effects in the two-dimensional hole gases by applying the magnetic field in the xy plane, and then explore the dependence of Hall conductivity and Hall resistance on the Fermi level and the magnetic field (both magnitude and direction) and related longitudinal carrier transport properties.