SrTiO 3

1. SrTiO3 Tomáš Bzdušek for Advanced Solid State Physics

2. Where are we now?

3. Structure of SrTiO3 Vertices – Sr Cube center – Ti Facet centers – O Sides (simple cubic) Notice this octahedron! http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

4. What happens below critical temperature? Simple cubic  Tetragonal http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

5. Whathappensbelow critical temperature? http://cst-www.nrl.navy.mil/ResearchAreas/Ferroelectrics/

6. Whathappensbelow critical temperature? http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

7. More about phase transition in SrTiO3(à la outline) • Experimental evidence • What drives the phase transition? • Is case of SrTiO3 exceptional?

8. Experimental evidence

9. Lossofsymmetry = new Braggpeaks • High temperature

10. Lossofsymmetry = new Braggpeaks Destructive interference!

11. Loss of symmetry in SrTiO3 Blue octahedra clockwiserotated Greenoctahedra counterclockwiserotated

12. Loss of symmetry in SrTiO3 real space momentum space High-T phase: Low-T phase:

13. Experimental verification • Risingintensityof a new Braggpeakthatappersbelowcriticaltemperature. G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).

14. Hypothesis of “soft mode” • There might exist an optical phonon with vanishing frequency: • UnderTc, thecrystalisunstableagainstthisphonon and „crashes“ intoa new structure. as

15. Inelastic neutron scattering

16. Inelastic scattering & “Soft mode” G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).

17. Soft mode verification R. A. Cowley, The Phase Transition of Strontium Titanate, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 384, 2799 (1996)

18. What drives the phase transition?

19. Phonon theory • The simplest phonon theory is quadratic • Widely used, though sometimes insufficient: • Phonon frequencies independent of temperature • No thermal expansion of a crystal • Higher corrections necessary: • Example: To obtain thermal expansion we need 3rd order expansion of potential.

20. A “toy model” • To obtain soft mode we need 4th order expansion of potential with specific properties. M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)

21. Order-disorder limit • If potential depth is much larger than coupling constant,  atoms always sit in one of the minima. • Yet another application of the Ising model!

22. Displacive limit • If potential depth is much smaller than coupling constant,  atoms’ positions change smoothly • This is the case of SrTiO3.

23. Theory vs. experiments • Detailed computation predicts soft mode vanishing as . • Below Tc, the crystal changes structure and new phonon branches appear. M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)

24. Is case of Strontium Titanite exceptional?

25. Definitely not! And many others (screenshot of part of long list of displacive phase transitions in Dove’s article).

26. Example: Ferroelectrics • Atoms move to create a net dipole moment • SrTiO3 also approaches ferroelectric transition at absolute zero. http://department.fzu.cz/lts/en/res-ferro.htm http://en.wikipedia.org/wiki/Ferroelectricity

27. Used literature • G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969). • R. A. Cowley, The Phase Transition of Strontium Titanate, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 384, 2799 (1996) • M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997) • Some cited images from Internet and even more own ones.