Tuning Spin-Orbit Coupling and Superconductivity at the ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ Interface: A Magnetotransport Study

The superconducting transition temperature $T_c$ of the ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ interface was varied by the electric field effect. The anisotropy of the upper critical field and the normal-state magnetotransport were studied as a function of gate voltage. The spin-orbit coupling energy ${ϵ}_{\mathrm{SO}}$ is extracted. This tunable energy scale is used to explain the strong gate dependence of the mobility and of the anomalous Hall signal observed. ${ϵ}_{\mathrm{SO}}$ follows $T_c$ for the electric field range under study.

Figure 1

(a) Normalized sheet resistance versus temperature for the various gate voltages (from left to right) $V_g=50\mathrm{V}$, as-grown state, 10 V, $-10\mathrm{V}$, $-50\mathrm{V}$ color and shape code applies to all graphs in the Letter. (b) Resistivity versus the perpendicular magnetic field. Inset: zoom on the low field region where superconductivity is suppressed.

Figure 2

Sheet resistance versus the magnetic field applied parallel to the interface and current for various charge densities.

Figure 3

(a) The parallel upper critical field $H_{c\parallel }$ versus $k_B{T}_c$ while $V_g$ is varied. The dashed line represents the expected behavior for the paramagnetic limit. (b) ${ϵ}_{\mathrm{SO}}$ extracted from $H^{*}$ [see Fig. 2], and calculated from the measured superconducting properties ($H_{c2\parallel }$ and $T_c$) [16], versus $k_B{T}_c$. The right axes presents $\Delta R$, which scales with ${ϵ}_{\mathrm{SO}}$ as expected.

Figure 4

(a) Normalized resistance as a function of perpendicular magnetic field. Data are taken while rotating the sample in a constant magnetic field of 18 T. (b) Hall resistivity after subtraction of a linear fit for high fields (AHE). (c) The AHE for $n=4.4\times {10}^{13}{\mathrm{cm}}^{-2}$ while $H$ is scanned, and while rotating the sample at a constant field.