  Multiferroic van der Waals (vdW) heterostrucutres offers an exciting route
towards novel nanoelectronics and spintronics device technology. Here we
investigate the electronic and transport properties of multiferroic vdW
heterostructure composed of ferromagnetic FeCl$_2$ monolayer and ferroelectric
Sc$_2$CO$_2$ monolayer using first-principles density functional theory and
quantum transport simulations. We show that FeCl$_2$/Sc$_2$CO$_2$
heterostructure can be reversibly switched from semiconducting to half-metallic
behavior by electrically modulating the ferroelectric polarization states of
Sc$_2$CO$_2$. Intriguingly, the half-metallic phase exhibits a Type-III broken
gap band alignment, which can be beneficial for tunnelling field-effect
transistor application. We perform a quantum transport simulation, based on a
\emph{proof-of-concept} two-terminal nanodevice, to demonstrate
all-electric-controlled valving effects uniquely enabled by the nonvolatile
ferroelectric switching of the heterostructure. These findings unravels the
potential of FeCl$_2$/Sc$_2$CO$_2$ vdW heterostructures as a building block for
designing a next generation of ultimately compact information processing, data
storage and spintronics devices.
