Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces

The quasi-two-dimensional electron gas found at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface offers exciting new functionalities, such as tunable superconductivity, and has been proposed as a new nanoelectronics fabrication platform. Here we lay out a new example of an electronic property arising from the interfacial breaking of inversion symmetry, namely, a large Rashba spin-orbit interaction, whose magnitude can be modulated by the application of an external electric field. By means of magnetotransport experiments we explore the evolution of the spin-orbit coupling across the phase diagram of the system. We uncover a steep rise in Rashba interaction occurring around the doping level where a quantum critical point separates the insulating and superconducting ground states of the system.

Figure 1

Modulation of the transport properties of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface under electric and magnetic fields. (a) Magnetoconductance $[\sigma (H)-\sigma (H=0)]/\sigma (H=0)$ ($\sigma$ being the sheet conductance, and $H$ the applied magnetic field) measured at 1.5 K in perpendicular magnetic field for different applied gate voltages. (b) Sheet resistance ($R_0$) modulation resulting from the field effect measured at 1.5 K. (c) Field effect modulation of the diffusion coefficient $D$ estimated at 1.5 K.

Figure 2

Analysis of the magnetoconductivity of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. (a) Best fits according to the Maekawa-Fukuyama theory of the variation of conductance $\Delta \sigma$, normalized with respect to $e^2/\pi h$, for different gate voltages. (b) Gate voltage dependence of the fitting parameters $H_i$ (red dots) and $H_{\mathrm{so}}$ (blue squares). The lines are a guide to the eye. (c) Left axis, purple diamonds: gate voltage dependence of the electrons $g$ factor $g$. The line is a guide to the eye. Right axis, blue triangles: superconducting critical temperature $T_c$ as a function of gate voltage for the same sample.

Figure 3

Rashba control of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface electronic phase diagram. (a) Inelastic relaxation time ${\tau }_i$ (red circles) and spin relaxation time ${\tau }_{\mathrm{so}}$ (blue squares) as a function of gate voltage plotted on a logarithmic time scale. The lines are a guide to the eye. Prediction of the spin relaxation time as a function of gate voltage based on the Elliott relation (open circles). (b) Spin relaxation time vs elastic scattering rate showing consistency with the D’yakonov-Perel’ mechanism. (c) Left axis, red triangles: field effect modulation of the Rashba spin splitting $\Delta$. Right axis, gray diamonds: field effect modulation of the Rashba coupling constant $\alpha$. (d) Superconducting critical temperature $T_c$ as a function of gate voltage for the same sample. Note that the crossing of the inelastic and spin relaxation times occurs at the quantum critical point.