We propose a new topological quantum state of matter---the two-dimensional (2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin-polarized 2D Weyl fermions. We predict its realization in the ground state of monolayer PtCl$_3$. We show that the material is a half metal with an in-plane magnetization, and its Fermi surface consists of a pair of fully spin-polarized Weyl points protected by a mirror symmetry, which are robust against spin-orbit coupling. Remarkably, we show that the WHS state is a critical state at the topological phase transition between two quantum anomalous Hall insulator phases with opposite Chern numbers, such that a switching between quantum anomalous Hall states can be readily achieved by rotating the magnetization direction. Our findings demonstrate that WHS offers new opportunity to control the chiral edge channels, which will be useful for designing new topological electronic devices.
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