## 6 Conclusions and Perspectives  
The first measurements of the variation in the longitudinal acoustic velocity and the optical refractive index in thin films deposited on different substrates across the rhombohedral to tetragonal structural phase transition induced by element substitution are reported thanks to a multi-technique approach. They reveal a strong elastic anomaly, i.e., pronounced minimum of longitudinal sound velocity, in the vicinity of the structural transition. The strength of the related optical anomaly, i.e., of the maximum in the refractive index, was found to be significantly dependent on the particular substrate influencing the parameters of the thin films. Our results (together with earlier ones [12; 13]) demonstrating that BPFMO films at the structure transition composition show the strongest ferromagnetism and superior ferroelectric properties) indicate that BFO-based films with compositions near phase boundaries might exhibit maxima in piezoelectric and piezomagnetic properties and are promising materials for multifunctional applications. The challenging perspective for the TDBS technique in combination with the other techniques would be their application for the diagnostics of the variations of the acousto-optical interaction efficiency (controlled by the photoelastic parameter) across the structural transitions in thin films. Research in this direction could potentially reveal films with superior efficiency in the acousto-optical modulation of light for the future information and communication technologies. Conceptualization, V.G., D.W., S.R., and P.R. ; methodology, V.G. and S.R. ; software, S.R. ; validation, N.C., E.d.L.S., A.B., and N.D.; formal analysis, S.R., N.C., E.d.L.S., A.B., N.D., A.R., Z.W., and Q.J. ; investigation, A.L., S.A., N.C., E.d.L.S., A.B., N.D., Z.W., Q.J., M.K., A.R., and G.V. ; resources, D.W. and Z.W. ; writing--original draft preparation, V.G., S.R., A.B., N.D., and Z.W. ; writing--review and editing, V.G., S.R., A.B., N.D., Z.W., and P.R. ; visualization, S.R., N.C., A.B., N.D., Z.W., and A.R. ; supervision, D.W., V.G., and P.R. ; project administration, V.G. and D.W.; funding acquisition, P.R., V.G., and D.W. This research was funded by LE MANS ACOUSTIQUE, in the frame of the project \"Optically controlled ferroelectric transducers\". The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Appendix A Procedure of the (Bi\({}_{1-x}\)Pr\({}_{x}\))(Fe\({}_{0.95}\)Mn\({}_{0.05}\)O\({}_{3}\) (BPFMO) Film Deposition  
The (Bi\({}_{1-x}\)Pr\({}_{x}\))(Fe\({}_{0.95}\)Mn\({}_{0.05}\))O\({}_{3}\) thin films were deposited on Si and single-crystalline LaAlO\({}_{3}\) (100) substrates using chemical solution deposition. The precursor solutions were prepared by dissolving Bi(NO\({}_{3}\))\({}_{3}\)\(\cdot\)5H\({}_{2}\)O (99.99%), Fe(NO\({}_{3}\))\({}_{3}\)\(\cdot\)9H\({}_{2}\)O (99.9%), Mn(CH\({}_{3}\)COO)\({}_{2}\)\(\cdot\)2H\({}_{2}\)O (99.99%), and Pr(NO\({}_{3}\))\({}_{3}\)\(\cdot\)6H\({}_{2}\)O (99.99%) in acetic acid (99.8%) and ethylene glycol (99%). Citric acid (99.5%), twice the amount of the total metallic ions in solutions, was added as a chelating agent. The final concentrations were adjusted to 0.2 mol/l. Films with various Pr concentrations were obtained by varying the amounts of Pr(NO\({}_{3}\))\({}_{3}\)\(\cdot\)6H\({}_{2}\)O in the solutions. The BPFMO films were deposited onto substrates by spin coating at 4000 rpm for 30 s. The wet films were baked at 300 \({}^{\circ}\)C, pyrolyzed at 400 \({}^{\circ}\)C for 10 min in flowing O\({}_{2}\), and then annealed at 525 \({}^{\circ}\)C for 3 min in flowing N\({}_{2}\). These steps were repeated for 12 times to reach the designed film thickness. The final annealing was performed at 525 \({}^{\circ}\)C for 30 min in N\({}_{2}\) to achieve better crystallinity.