Gate-Controlled Spin Injection at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interfaces

We report results of electrical spin injection at the high-mobility quasi-two-dimensional electron system (2-DES) that forms at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. In a nonlocal, three-terminal measurement geometry, we analyze the voltage variation associated with the precession of the injected spin accumulation driven by perpendicular or transverse magnetic fields (Hanle and inverted Hanle effect). The influence of bias and back-gate voltages reveals that the spin accumulation signal is amplified by resonant tunneling through localized states in the ${\mathrm{LaAlO}}_3$ strongly coupled to the 2-DES by tunneling transfer.

Figure 1

(a) Sketch of the devices for 3-T Hanle measurements with the magnetic field applied perpendicular or parallel to the sample plane. A gate voltage $V_g$ can be applied between the back of the STO crystal and the LAO/STO 2-DES. “a-LAO” stands for amorphous ${\mathrm{LaAlO}}_3$, “$\Omega$” for Ohmic contact, and the 2-DES is shown in green. $M$ is the in-plane Co electrode magnetization. (b) Typical $I$ vs. $V$ characteristics of a $\mathrm{Co}/{\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ ($L=100\mu \mathrm{m}$, $W=300\mu \mathrm{m}$) sized junction measured at 12 K.

Figure 2

(a) Temperature $T$ dependence of the junction $RA$ product measured at $I=+100$, $+50$ and $-50\mathrm{nA}$ in black; the colored symbols correspond to the $RA$ value for $I=+20\mathrm{nA}$ as shown in (c) We used $\star$ to indicate the observation of an Hanle effect and $\times$ if not. (b) $RA$ product and voltage change as a function of the perpendicular external magnetic field $H_{\perp }$ (Hanle measurement). Lines correspond to Lorentzian fits of the data with (solid line) or without (dashed line) a parabolic background. (c) Hanle data acquired at different temperatures for $I=+20\mathrm{nA}$ except for 2 K and 150 K for which $I=+50\mathrm{nA}$. The curves are vertically offset for the sake of clarity. (d) MR with the magnetic field perpendicular or parallel to the sample plane at 12 K for the same injected current of $I=+50\mathrm{nA}$. The dashed lines correspond to Lorentzian fits without the parabolic background.

Figure 3

Sketch of the band structure and electronic localized states in the barrier for (a) negative and (b) positive measurement bias on the $FM$ electrode. The dashed line is the Fermi level in STO, the grey area represents the filled states of Co. (c) Illustration of our model inspired from Ref. 14 whereby electrons transit via discrete states in which the spin is depolarized by a field $H_r$. Physical parameters are defined in the text.

Figure 4

(a) MR of the $\mathrm{Co}/\mathrm{LAO}/\mathrm{STO}$ structure in $H_{\perp }$ and $H_{||}$ configurations for different gate voltage $V_g$ at 2 K. (b) Total Hanle signal $\Delta R_{H}A$ (evaluated at 0.25 T) vs measurement bias $V$ applied across the $\mathrm{Co}/\mathrm{LAO}/\mathrm{STO}$ junction at different $V_g$. Arrows indicate $\Delta R_H^{\max }A$ (c) Sketch of the 2-DES band structure evolution vs $V_g$, illustrating the loss of carrier confinement in the 2-DES (decrease of $k^{\perp }$) as $V_g$ increases. (d) $V_g$ dependence of the various resistances, showing the singular increase of the total spin signal $\Delta R_H^{\max }A$ vs $V_g$, whereas the sheet resistance of the channel $R_{\square }$ decreases as expected [5, 6, 7, 8, 9].