  Correlated oxides and related heterostructures are intriguing for developing
future multifunctional devices by exploiting their exotic properties, but their
integration with other materials, especially on Si-based platforms, is
challenging. Here, van der Waals heterostructures of
La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO), a correlated manganite perovskite, and
MoS$_2$ are demonstrated on Si substrates with multiple functions. To overcome
the problems due to the incompatible growth process, technologies involving
freestanding LSMO membranes and van der Waals force-mediated transfer are used
to fabricate the LSMO-MoS$_2$ heterostructures. The LSMO-MoS$_2$
heterostructures exhibit a gate-tunable rectifying behavior, based on which
metal-semiconductor field-effect transistors (MESFETs) with on-off ratios of
over 104 can be achieved. The LSMO-MoS$_2$ heterostructures can function as
photodiodes displaying considerable open-circuit voltages and photocurrents. In
addition, the colossal magnetoresistance of LSMO endows the LSMO-MoS$_2$
heterostructures with an electrically tunable magnetoresponse at room
temperature. This work not only proves the applicability of the LSMO-MoS$_2$
heterostructure devices on Si-based platform but also demonstrates a paradigm
to create multifunctional heterostructures from materials with disparate
properties.
