  In addition to spin, electrons in many materials possess an additional
pseudo-spin degree of freedom known as 'valley'. In materials where the spin
and valley degrees of freedom are weakly coupled, they can be both excited and
controlled independently. In this work, we study a model describing the
interplay of the spin and valley Hall effects in such two-dimensional
materials. We demonstrate the emergence of an additional longitudinal neutral
current that is both spin and valley polarized. The additional neutral current
allows to control the spin density by tuning the magnitude of the valley Hall
effect. In addition, the interplay of the two effects can suppress the Hanle
effect, that is, the oscillation of the nonlocal resistance of a Hall bar
device with in-plane magnetic field. The latter observation provides a possible
explanation for the absence of the Hanle effect in a number of recent
experiments. Our work opens also the possibility to engineer the conversion
between the valley and spin degrees of freedom in two-dimensional materials.
