  We uncover two anomalous features in the nonlocal transport behavior of
two-dimensional metallic materials with spin-orbit coupling. Firstly, the
nonlocal resistance can have negative values and oscillate with distance, even
in the absence of a magnetic field. Secondly, the oscillations of the nonlocal
resistance under an applied in-plane magnetic field (Hanle effect) can be
asymmetric under field reversal. Both features are produced by direct
magnetoelectric coupling, which is possible in materials with broken inversion
symmetry but was not included in previous spin diffusion theories of nonlocal
transport. These effects can be used to identify the relative contributions of
different spin-charge conversion mechanisms. They should be observable in
adatom-functionalized graphene, and may provide the reason for discrepancies in
recent nonlocal transport experiments on graphene.
