  Half topological states of matter and two-dimensional (2D) magnetism have
gained much attention recently. In this paper, we propose a special topological
semimetal phase called a 2D half Chern-Weyl semimetal (HCWS), which is a 2D
magnetic Weyl semimetal bound to the half Chern insulator phase by symmetry,
and the two phases can be converted to each other by manipulating the
magnetization direction. We provide the symmetry conditions to realize this
state in 2D systems with multiple screw axes. Tight-binding models with
multiple basis and a predicted 2D material, monolayer TiTe, are shown as the
concrete examples for HCWSs. The TiTe monolayer was shown to have a high
ferremagnetic Curie temperature (~966 K) as well as a Coulomb
correlation-enhanced spin-orbit coupling (SOC), and further demonstrates the
effect of correlation-enhanced SOC on magnetocrystalline anisotropy energy and
energy gap opening. Our work reveals a state with switchable and spin-resolved
half body charge currents as well as half boundary charge currents, and will
provide a platform for novel and high-performance topological spintronics
devices.
