Intrinsic Quantum Anomalous Hall Effect with In-Plane Magnetization: Searching Rule and Material Prediction

So far, most theoretically predicted and experimentally confirmed quantum anomalous Hall effects (QAHEs) are limited in two-dimensional (2D) materials with out-of-plane magnetization. In this Letter, starting from 2D nodal-line semimetal, a general rule for searching QAHE with in-plane magnetization is mapped out. Because of spin-orbital coupling, we found that the magnetization will prefer an in-plane orientation if the orbital of degenerate nodal-line states at the Fermi level have the same absolute value of magnetic quantum number. Moreover, depending on the broken or conserved mirror symmetry, either a QAHE or 2D semimetal can be realized. Based on first principles calculations, we further predict a real material of monolayer LaCl to be an intrinsic QAHE with in-plane magnetization. By tuning the directions of in-plane magnetization, the QAHE in LaCl demonstrates a threefold rotational symmetry with a Chern number of either +1 or -1, and the transition point is characterized by a 2D semimetal phase. All these features are quantitatively reproduced by tight-binding model calculations, revealing the underlying physics clearly. Our results greatly extend the scope for material classes of QAHE and hence stimulate immediate experimental interest.