Nonlinear valley and spin valves in bilayer graphene

Nonlinear transport plays a vital role in probing the quantum geometry of Bloch electrons, valley chirality, and carrier scattering mechanisms. The nonlinear Hall effect, characterized by a nonlinear scaling of Hall voltage with longitudinal current, has been explored to reveal the Berry curvature and quantum metric--related physics. In this work, we extend the study of nonlinear transport to spin and valley degrees of freedom. Using bilayer graphene devices with ${\mathrm{Fe}}_{3}{\mathrm{Ge}\mathrm{Te}}_{2}$ contacts, we observe a second-order nonlinear spin current exhibiting spin-valve-like behavior. By tracking magnetic moment precession under an in-plane magnetic field, we identify a significantly enhanced critical magnetic field required for in-plane rotation, suggesting out-of-plane valley polarization induced by ferromagnetic proximity. These findings offer deep insights into the interplay of valley and spin in second-order nonlinear transport, opening avenues for promising device applications.