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The magnitude of spin accumulation created in semiconductors by electricalinjection of spin-polarized electrons from a ferromagnetic tunnel contact isinvestigated, focusing on how the spin signal detected in a Hanle measurementvaries with the thickness of the tunnel oxide. An extensive set ofspin-transport data for Si and Ge magnetic tunnel devices reveals a scalingwith the tunnel resistance that violates the core feature of availabletheories, namely, the linear proportionality of the spin voltage to theinjected spin current density. Instead, an anomalous scaling of the spin signalwith the tunnel resistance is observed, following a power-law with an exponentbetween 0.75 and 1 over 6 decades. The scaling extends to tunnel resistancevalues larger than 10$^{9}$ $\Omega\mu m^2$, far beyond the regime where theclassical impedance mismatch plays a role. This scaling is incompatible withexisting theory for direct tunnel injection of spins into the semiconductor. Italso demonstrates conclusively that the large spin signal does not originatefrom two-step tunneling via localized states near the oxide/semiconductorinterface. Control experiments on devices with a non-magnetic metal (Ru)electrode, instead of the semiconductor, exhibit no Hanle spin signal, showingthat spin accumulation in localized states within the tunnel barrier is alsonot responsible. Control devices in which the spin current is removed byinserting a non-magnetic interlayer exhibit no Hanle signals either, provingthat the spin signals observed in the standard devices are genuine andoriginate from spin-polarized tunneling and the resulting spin accumulation.Altogether, the scaling results suggest that the spin signal is proportional tothe applied bias voltage, rather than the (spin) current.

Anomalous scaling of spin accumulation in ferromagnetic tunnel devices with silicon and germanium