Experimental Evidence of Cubic Rashba Effect in an Inversion-Symmetric Oxide

We present evidence of cubic Rashba spin splitting in a quasi-two-dimensional electron gas formed at a surface of (001) ${\mathrm{SrTiO}}_{3}$ single crystal from the weak localization or antilocalization (WAL) analysis of the low-temperature magnetoresistance. Our WAL data were well fitted by the model assuming ${m}_{j}=\ifmmode\pm\else\textpm\fi{}3/2$ for the spin-split pair, in which $2\ensuremath{\pi}$ rotation of the electron wave vector ${\mathbf{k}}_{\ensuremath{\parallel}}$ in the ${k}_{x}\mathrm{\text{\ensuremath{-}}}{k}_{y}$ plane accompanies $6\ensuremath{\pi}$ rotation of the spin quantization axis. This finding pertains to the $p$ symmetry of the ${t}_{2g}$ electronic band derived from $d$ electrons in ${\mathrm{SrTiO}}_{3}$, which provides insights into the surface electronic state of (001) ${\mathrm{SrTiO}}_{3}$.