Fig. 4: R-ARPES measurement results for the band dispersion and Fermi surface with the theoretical curves and spin orientations, and a comparison between the experimental λ_IEE and theoretical λ_IEE.

a Band dispersion of a reference sample LTO (3 u.c.)/STO along k_x measured by R-ARPES. The 2DEG states are observed using the resonant photon energy for the Ti L₃ absorption edge of the Ti³⁺ component (hν = 459.7 eV). The solid and broken curves represent the band dispersions calculated by the effective tight-binding model. The inset is the enlarged band dispersion of the calculation near the crossing point of the d_xy and d_yz bands. The dotted line of the inset corresponds to the Fermi level used for the calculation of λ_IEE in the LSMO/LTO/STO sample (E’_F = –102 meV). Here, E_F and E’_F are the Fermi levels of LTO/STO obtained by the R-ARPES measurement and the Hall effect measurement, respectively (see Supplementary Note 4). b Fermi surface of the reference sample LTO (3 u.c.)/STO obtained by R-ARPES. Although it is not clear, the Fermi surface of the thin LTO layer, which is considered to be small due to its small carrier concentration, may be partially overlapped with the Fermi surface of the 2DEG at around the center of the k_x−k_y plane. In this measurement, the Fermi surface elongated in the k_y direction is visible, but the surface elongated in the k_x direction is almost not, due to the experimental geometry of the ARPES measurements⁴⁸. The solid and broken curves are the Fermi surfaces calculated by the effective tight-binding model at E_F = 0 meV. c Temperature T dependence of experimental λ_IEE for the LSMO/LTO/STO sample and calculated λ_IEE for Δ_z = 15, 20 and 25 meV with Δ_ASO fixed at 15 meV. d Calculated Fermi surface and spin expectation values (arrows) at E’_F = –102 meV by the effective tight-binding model.