  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.
