1：Experimental Design and Method Selection:

BaTiO3/Ba50Sr50TiO3 (BT/BST) and BaTiO3/Ba50Sr50TiO3/SrTiO3 (BT/BST/ST) SLs were grown onto (001) single-crystal MgO substrates via the pulsed laser deposition by the alternating focus of a laser beam on BT, BST, and ST targets.

2：Sample Selection and Data Sources:

The modulation period Λ of BT/BST layers in a two-layer BT/BST SL was 130 ? (the thickness of individual layers was 65 ?) and that of BT/BST/ST layers in a three-layer BT/BST/ST SL enriched 150 ? (resulting in a 50-? thickness of the constituting layers). The total thickness of heterostructures was 1 μm.

3：List of Experimental Equipment and Materials:

Raman spectra were excited at room temperature with an argon laser (λ =

4：5 nm) and recorded by an Invia Reflex Renishaw spectrometer equipped with a near-excitation tunable (NExT) filter for the low-frequency spectral range analysis. The exciting radiation was focused atop a sample with a Leica optical microscope in a spot with a diameter of 2 μm. Experimental Procedures and Operational Workflow:

5 Polarized Raman spectra were collected on samples oriented with respect to crystallographic axes of substrates as X || 100, Y || 010, and Z ||

5：Spectra with pronounced E-type soft modes were acquired in the side-view backscattering, at which the wave vector of the incident beam is parallel to the substrate, and the polarization of incident and scattered light is parallel or perpendicular to the Z axis of the film. Data Analysis Methods:

0 The analysis focused on the behavior of E(1TO) line which is attributed to the transverse optical vibration of soft modes E that split in various components with reducing symmetry of ABO3-type perovskites.