SrTiO3Tomáš Bzdušekfor Advanced Solid State Physics

Where are we now?

Structure of SrTiO3

Vertices – SrCube center – TiFacet centers – O

http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

Notice this octahedron!

Sides (simple cubic)

What happens below critical temperature?

Simple cubic Tetragonalhttp://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

What happens below critical temperature?

http://cst-www.nrl.navy.mil/ResearchAreas/Ferroelectrics/

What happens below critical temperature?

http://hasylab.desy.de/news__events/research_highlights/perovskite_like_crystal_in_an_electric_field/index_eng.html

More about phase transition in SrTiO3(à la outline)

Experimental evidence

What drives the phase transition?

Is case of SrTiO3 exceptional?

EXPERIMENTAL EVIDENCE

High temperature

Loss of symmetry = new Bragg peaks

Loss of symmetry = new Bragg peaks

Destructive interferenc

e!

Loss of symmetry in SrTiO3

Blue octahedraclockwise rotated

Green octahedracounterclockwise

rotated

Loss of symmetry in SrTiO3

High-T phase:

Low-T phase:

real space momentum space

Experimental verification

G. Shirane and Y. Yamada, Lattice-dynamical study of 110 degrees K phase transition in SrTiO3, Phys. Rev. 177, 858 (1969).

• Rising intensity of a new Bragg peak that appers below critical temperature.

Hypothesis of “soft mode”There might exist an optical

phonon with vanishing frequency:

Under Tc, the crystal is unstable against this phonon and „crashes“ into a new structure.

as

Inelastic neutron scattering

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).

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)

WHAT DRIVES THE PHASE TRANSITION?

Phonon theoryThe simplest phonon theory is

quadraticWidely 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.

A “toy model”

M. T. Dove Theory of displacive phase transitions in minerals, Am. Miner. 82, 213, (1997)

To obtain soft mode we need 4th order expansion of potential with specific properties.

Order-disorder limitIf potential depth is much larger than

coupling constant, atoms always sit in one of the minima.

Yet another application of the Ising model!

Displacive limitIf potential depth is much smaller

than coupling constant, atoms’ positions change smoothly

This is the case of SrTiO3.

Theory vs. experiments

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)

Detailed computation predicts soft mode vanishing as .

IS CASE OF STRONTIUM TITANITE EXCEPTIONAL?

And many others (screenshot of part of long list of displacive phase transitions in Dove’s article).

Definitely not!

Example: FerroelectricsAtoms move to create a net dipole moment

SrTiO3 also approaches ferroelectric transition at absolute zero.http://department.fzu.cz/lts/en/res-ferro.htmhttp://en.wikipedia.org/wiki/Ferroelectricity

Used literatureG. 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.