Nonlinear spin and orbital Edelstein effect in WTe2

Abstract

In materials with spin-momentum locked spin textures, such as Rashba states and topological surface states, the current-induced shift of the Fermi contour in the k space leads to spin polarization, known as the Edelstein effect, which depends linearly on the applied current. However, its nonlinear counterpart has not yet been discovered. Here, we report the observation of the nonlinear Edelstein effect in few-layer WTe2. Under a current bias, an out-of-plane magnetization is induced in WTe2, which is electrically probed using an Fe3GeTe2 electrode, a van der Waals ferromagnet with perpendicular magnetic anisotropy. Notably, with an applied ac at frequency ω, an induced magnetization with second-harmonic response at frequency 2ω is observed, and its magnitude demonstrates a quadratic dependence on the applied current, characteristic of the nonlinear Edelstein effect. This phenomenon is well explained by the current-induced orbital magnetization via the Berry connection polarizability tensors in WTe2. The orbital degree of freedom plays the primary role in the observed nonlinear Edelstein effect, that is, the nonlinear orbital Edelstein effect. This can, in turn, give rise to a nonlinear spin Edelstein effect through spin-orbit coupling.