  Low-energy coherent transport and Goos-H\"{a}nchen (GH) lateral shift of
valley electrons in planar heterojunctions composed of normal MoS$_2$ and
ferromagnetic WS$_2$ monolayers are theoretically investigated. Two types of
heterojunctions in the forms of WS$_2$/MoS$_2$/WS$_2$ (type-A) and
MoS$_2$/WS$_2$/MoS$_2$ (type-B) with incident electrons in MoS$_2$ region are
considered in which the lateral shift of electrons is induced by band
alignments of the two constituent semiconductors. It is shown that the type-A
heterojunction can act as an electron waveguide due to electron confinement
between the two WS$_2$/MoS$_2$ interfaces which cause the incident electrons
with an appropriate incidence angle to propagate along the interfaces. In this
case the spin- and valley-dependent GH shifts of totally reflected electrons
from the interface lead to separated electrons with distinct spin-valley
indexes after traveling a sufficiently long distance. In type-B heterojunction,
however, transmission resonances occur for incident electron beams passing
through the structure, and large spin- and valley-dependent lateral shift
values in propagating states can be achieved. Consequently, the transmitted
electrons are spatially well-separated into electrons with distinct spin-valley
indexes. Our findings reveal that the planar heterojunctions of transition
metal dichalcogenides can be utilized as spin-valley beam filter and/or
splitter without external gating.
