Extended Data Fig. 7: Equilibrium characterizations of (PbTiO₃)₁₆/(SrTiO₃)₁₆ superlattice.

a, Room-temperature RSM of the superlattice grown on DSO substrate, cutting through the substrate specular 004 peak, which shows vortex (V) and FE superlattice diffraction peaks in the q_x–q_z plane. The satellites (V Sat) due to the in-plane vortex ordering appear along the q_x direction around the corresponding superlattice (V) peaks. b, The measured average lattice parameters with linear fits for the vortex and FE structures as a function of temperature. The error bars represent systematic errors of the measurement. c, Room-temperature RSM of the superlattice grown on Sr₂Al_0.3Ga_0.7TaO₆ (SAGT) substrate, cutting through the substrate specular 002 peak, which shows the vortex SL diffraction peaks and satellites. d, Room-temperature imaginary dielectric constant extracted from the THz time-domain absorption spectroscopy measurements of superlattices grown on DSO and SAGT substrates. The error bars represent the estimated experimental errors in the frequency ranges of the shaded and unshaded regimes.