Electrical Spin Injection into High Mobility 2D Systems

We report on spin injection into a high mobility 2D electron system confined at an $(\mathrm{Al},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ interface, using (Ga,Mn)As Esaki diode contacts as spin aligners. We measured a clear nonlocal spin valve signal, which varies nonmonotonically with the applied bias voltage. The magnitude of the signal cannot be described by the standard spin drift-diffusion model, because at maximum this would require the spin polarization of the injected current to be much larger than 100%, which is unphysical. A strong correlation of the spin signal with contact width and electron mean free path suggests that ballistic transport in the 2D region below ferromagnetic contacts should be taken into account to fully describe the results.

Figure 1

(a) Sample layout and the main measurement configuration described in the text. (b) The layer sequence of the device; on the left- and right-hand sides we show simulated conduction band edge profiles (black lines) together with the electrons’ density (red lines) at $T=4.2\mathrm{K}$ for a complete layer stack and with the highly doped top layers etched away, respectively. (c) Magnetotransport measurements on a standard Hall bar device. (d) $I\text{−}V$ characteristics of contacts 2 and 3 taken in the three-terminal geometry. The arrows mark positions of “the Esaki kink” for the each curve.

Figure 2

(a) Nonlocal voltage at contact 3 for $I_{21}=-15\mu \mathrm{A}$ versus in-plane magnetic field $B_x$ at $T=3.8\mathrm{K}$; field-dependent background has been removed from the raw data. (b) Bias dependence of the amplitude $\mathrm{\Delta }{R}_{\text{NL}}$ of the NLSV signal plotted versus $V_{3T}$ for the narrow-wide (red circles) and wide-narrow (blue) configurations, as defined in the text. Sketches on the left-hand side show how the width of injector and detector contacts in the each configuration compares to the mean free path $l_{\text{mf}}$. Solid black lines correspond to the expected amplitude of the signal calculated using Eq. (1). We used $P_{\text{det}}=75\%$ and $P_{\text{inj}}=P_{\text{det}}$ at low bias. Inset: Bias dependence of the NLSV signal from a low mobility (In,Ga)As QW structure with $l_{\text{mf}}=0.55\mu \mathrm{m}$, for the narrow-wide configuration. (c) Temperature dependence of the NLSV signal’s amplitude for the narrow-wide configuration for three injector current values, marked with arrows in (b).

Figure 3

Possible tunneling processes, indicated by orange arrows, at different bias. Shown is the region of intermediate bulk states (3D), 2DEG, and depletion width $w_{\text{depl}}$. (a) Low negative bias: spins are injected into 2DEG via 3D bulk states. (b) High negative bias: spins are injected directly into 2DEG (3D region depleted). (c) Excess current regime: spins are extracted from the 2DEG via localized states in (Ga,Mn)As band gap, both with and without the contribution of 3D states.