  We theoretically show that the carrier transport in monolayer Fe3GeTe2
experiences a transition between anomalous Hall effect and spin Hall effect
when the spin polarization of disorders switches between out-of-plane and
in-plane. These Hall effects are allowed when the magnetization is polarized
in-plane, breaking the C3 rotation symmetry. The transition originates from the
selection rule of spin scattering, the strong spin-orbit coupling, and the van
Hove singularities near the Fermi surface. The scattering selection rule
tolerates the sign change of the disorder spin, which provides a convenient
method to detect the switching of antiferromagnetic insulators regardless of
the interfacial roughness in a heterostructure. This provides a convenient
platform for the study of 2D spintronics through various van-der-Waals
heterostructures.
