Mesoscopic Interference of Rotated Spins in Graphene Coupled to High-Spin–Orbit-Coupling Substrates

We explore the manifestations of spin rotation in graphene in proximity with two different types of high-spin–orbit-coupling (SOC) materials (ferromagnetic Co and nominally diamagnetic WSe₂). Using weak antilocalization (WAL) as a probe of the induced rotation, we demonstrate that spin interference exhibits a highly stochastic (nonself-averaging) character in the mesoscopic limit. At low temperatures (<20 K), the spin rotation is manifested as a zero-bias peak (or zero-bias anomaly, ZBA) in the differential conductance, a feature that, as expected for WAL, is suppressed by fairly modest magnetic fields (<∼10²mT). The ZBA moreover exhibits a stochastic variation when a gate voltage is used to sweep the Fermi level through the graphene bands, with ranges for which the antilocalization is either prominent or strongly suppressed. This mesoscopic character is exhibited by both of the studied systems, whose ZBA is also damped in similar fashion with increasing temperature. We thus provide fundamental insight into the nonensemble-averaged (nonself-averaged) character of spin interference in mesoscopic systems with strong SOC and, more specifically, into how the details of spin rotation are impacted by external gating. This understanding may ultimately enable the efficient modulation of spin currents in future spintronic devices.