Fig. 1
Spin splitting in the LAO//STO/LAO heterostructure. a Schematic structure of STO (left) and the asymmetric LAO//STO/LAO heterostructure (right) with a large built-in electric field Eb. b Band structure of t2g orbitals in the centrosymmetric STO layer. With compressive strain and spin–orbit interaction (SOI), the degenerate t2g orbitals are lifted with a splitting energy Δs. c Band structure of t2g orbitals with inversion symmetry broken as in the LAO//STO/LAO heterostructure. The degeneracy of the dxy and dyz/xz orbital is further lifted by the SOI. d Spin splitting energy of the t2g orbitals as a function of electron filling. The inset shows the k-linear and the cubic spin splitting of the corresponding orbitals
