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${}^9$ $\Omega \mu {\text{m}}^2$, far beyond the regime where the classical impedance mismatch or back flow into the ferromagnet play 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 show that spin accumulation in localized states within the tunnel barrier or artifacts are also not responsible. Altogether, the scaling results suggest that, contrary to all existing descriptions, the spin signal is proportional to the applied bias voltage, rather than the (spin) current.

Figure 1

Hanle detection of spin accumulation in semiconductor/oxide/ferromagnet tunnel devices. Shown are representative Hanle and inverted Hanle curves for magnetic field $B$ applied, respectively, perpendicular or parallel to the magnetization of the ferromagnet. Data are shown for $p$-type Si/Al${}_2$O${}_3$/Ni${}_{80}$Fe${}_{20}$ and $p$-type Si/MgO/Fe devices with different thickness of the tunnel barrier, all at 300 K. The vertical axis gives the spin-RA product, defined as $\Delta V_{\mathrm{Hanle}}/J$.

Figure 2

Scaling of Hanle spin signals in Si tunnel devices with amorphous Al${}_2$O${}_3$ barrier. (Left) tunnel resistance-area (RA) product vs Al${}_2$O${}_3$ thickness for $p$-type Si/Al${}_2$O${}_3$/Ni${}_{80}$Fe${}_{20}$ devices at 300 K. The extracted tunnel barrier height is 3.2 eV. (Middle) the corresponding spin RA product versus tunnel RA product. The solid line corresponds to a power law with exponent 0.75. (Right) data for similar devices but with $n$-type Si at 10 K. The solid line corresponds to a power law with exponent 0.82. The spin RA value is derived from the Hanle signal only, instead of the sum of the Hanle and inverted Hanle signals. See Appendix for additional data with different oxidation time ($p$-type) and Cs treated surfaces ($n$-type).

Figure 3

Scaling of Hanle spin signals for devices with MgO and $p$-type Si or Ge. (Left), spin RA product and tunnel RA product vs MgO thickness for $p$-type Si/MgO/Fe devices at 300 K. (Middle), corresponding spin RA product vs tunnel RA product for the same devices (pink symbols), together with data for $p$-type Si/Al${}_2$O${}_3$/Ni${}_{80}$Fe${}_{20}$ (blue symbols). For the three devices with the thinnest MgO barrier, the tunnel RA product is determined by extrapolation from the high thickness regime (dashed green line in the left panel) to remove the Schottky resistance. The solid line corresponds to a power law with exponent 0.75. (Right) Data for $p$-type Ge/MgO/Fe devices at 5 K. The spin RA product is the sum of the Hanle and inverted Hanle signal.

Figure 4

Attempts to fit the data by direct and two-step tunneling in parallel. The experimental data (pink symbols) for the junction resistance and spin RA product of $p$-type Si/MgO/Fe devices is compared with the model (solid lines) for three cases: (i) two-step tunneling only, (ii) direct tunneling only, and (iii) two-step tunneling and direct tunneling in parallel. In the top panels, two data points are given for the junction RA product of the three junctions with smallest MgO thickness; the larger value corresponds to the measured junction RA product, whereas the smaller value is obtained when the resistance of the Schottky barrier is subtracted.

Figure 5

Hanle linewidth vs tunnel resistance. The Hanle linewidth is characterized by an effective lifetime obtained from a fit of the Hanle curve using a Lorentzian. This time constant is a lower bound to the spin lifetime, as previously discussed [7, 25, 34]. The solid lines are guides to the eye.

Figure 6

Absence of spin accumulation in control tunnel devices with the Si replaced by nonmagnetic Ru metal. Shown are the Hanle and inverted Hanle signal for $p$-type Si/MgO/Fe devices, together with similar data on control devices with Fe/MgO/Ru structure (black circles and squares). Measurements were done at 300 K, and devices with a similar tunnel RA product are compared (10${}^5$ and 10${}^7$ $\Omega \mu {\text{m}}^2$ for the left and right panels, respectively). The absence of any spin signal in the metallic control devices proves the absence of spin accumulation in localized states within the MgO tunnel barrier.

Figure 7

Absence of spin signals in control tunnel devices with zero tunnel spin polarization. Shown are the Hanle and inverted Hanle signal for a control device with structure $p$-type Si/Al${}_2$O${}_3$/Au(10nm)/Ni${}_{80}$Fe${}_{20}$, in which the nonmagnetic Au interlayer causes the tunnel spin polarization to be zero. Measurements are done at room temperature with a constant current of $-$195 $\mu$A (hole injection condition). A constant bias voltage of about $-$172 mV was subtracted from the data.

Figure 8

Additional data on scaling of Hanle spin signals in tunnel devices with $n$-type and $p$-type Si. The open circles are the same data as in Fig. 2, whereas squares are additional data for devices with different oxidation time ($p$ type, left panel) and with Cs treated surfaces ($n$ type, right panel).