Anomalous scaling of spin accumulation in ferromagnetic tunnel devices with silicon and germanium
The magnitude of spin accumulation created in semiconductors by electrical injection of spin-polarized electrons from a ferromagnetic tunnel contact is investigated, focusing on how the spin signal detected in a Hanle measurement varies with the thickness of the tunnel oxide. An extensive set of spin-transport data for Si and Ge magnetic tunnel devices reveals a scaling with the tunnel resistance that violates the core feature of available theories, namely, the linear proportionality of the spin voltage to the injected spin current density. Instead, an anomalous scaling of the spin signal with the tunnel resistance is observed, following a power-law with an exponent between 0.75 and 1 over 6 decades. The scaling extends to tunnel resistance values larger than 10$^{9}$ $Ωμm^2$, far beyond the regime where the classical impedance mismatch plays a role. This scaling is incompatible with existing theory for direct tunnel injection of spins into the semiconductor. It also demonstrates conclusively that the large spin signal does not originate from two-step tunneling via localized states near the oxide/semiconductor interface. Control experiments on devices with a non-magnetic metal (Ru) electrode, instead of the semiconductor, exhibit no Hanle spin signal, showing that spin accumulation in localized states within the tunnel barrier is also not responsible. Control devices in which the spin current is removed by inserting a non-magnetic interlayer exhibit no Hanle signals either, proving that the spin signals observed in the standard devices are genuine and originate from spin-polarized tunneling and the resulting spin accumulation. Altogether, the scaling results suggest that the spin signal is proportional to the applied bias voltage, rather than the (spin) current.