1. Jeroen van den Brink Bond- versus site-centred ordering and possible ferroelectricity in manganites Leiden 12/08/2005

2. Outline Coupling of orbital degrees of freedom to: -- Lattice -- Spins -- Charge Orbital induced ferroelectricity in manganites Dima Efremov, JvdB, Daniel Khomskii, Nature Materials 3, 853 (2004)

3. Lottermoser et al., Nature 430, 541 (2004). Van Aken et al., Nature Mat. 3, 164 (2004). Kimura et al., Nature 426, 55 (2003). Hur et al., Nature 429, 392 (2004). Zheng et al., Science 303, 661 (2004). Fiebig et al., Nature 419, 818 (2002). Wang et al., Science 299, 1719 (2003). Spaladin, Physics World, April 2004. Magnetic Ferroelectrics Possible application: switching of magnetic bits by electric field Why study them? Fundamental interest: why rare? How to get around? Magnetic ferroelectrics are very rare!

4. What is a ferroelectric? dipole disorder ferroelectric Breaking of inversion symmetry

5. Valence electrons are in localized 3d orbitals R a correlated electron systems R a a R >>a R >> a conventional metals, semiconductors What is special about manganites? Do atomic physics first, include translation symmetry later

6. 3d orbitals of a Mn- ion e g orbitals t 2g orbitals Large Coulomb interaction between electrons on the ion Large Atomic Hund’s rule exchange Electron Spins Parallel

7. Orbitals behave like electron spins Compare orbitals and spins.... Orbitals are extra degree of freedom Impact on physical properties Order-disorder Thermodynamics Magnetism Lattice distortions Ferro-electricity Possible Multiferroic behavior

8. Orbitals and spins Similarities Angular momentum SU(2) algebra: [S x,S y ]=iS z Localized moment emergent from electron-electron interactions Spin-spin and orbital-orbital interaction due to superexchange Possibility of long range ordering

9. Orbitals and spins Differences SpinsOrbitals coupling to latticeWeakStrong Symmetry of HamiltionianHighLow ExcitationsGaplessGaped Frustration of orderSometimesAlways

10. 10 Mn 4+ / Mn 3+ Oxygen 2- La 3+ /Ca 2+ Perovskite crystal structure of La 1-x Ca x MnO 3

11. t 2g orbitals Cubic Crystal field splitting – – – – – – – – – – – – Local considerations 5x egeg t 2g 5x egeg t 2g Mn (3+) = 3d4 Mn (4+) = 3d3 e g orbitals Mn 4+ / Mn 3+

12. Orbital induced ferroelectricity in manganites with doping near x=1/2 Mn (3+) = 3d4 eg 1 Mn (4+) = 3d3 eg 0 E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955) Charge ordering Ferro zig-zag chains Magnetic CE-type order

13. Interplay orbital, spin and charge egeg t 2g Bond center Ferro t egeg t 2g Site center Antiferro JvdB, Khomskii, PRL 82, 1016 (1999) J AF Formally: DDEX model

14. DDEX model

15. Near x=0.4 : Bond-centered charge ordering A.Daoud-Aladine et al., PRL 89 97205 (2002) egeg t 2g Dimer

16. Near x=0.5 : Site-centered charge ordering E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)

17. Ferroelectric? x=0.5x=0.4 Site centered CO Bond centered CO Ferro-electric groundstate 0.4 < x < 0.5 intermediate It is allowed by symmetry:Can happenWill happen

18. Magnetic structure of Zener polaron? CE type ? Or: Jaffet-Kittel structure“orthogonal”structure

19. Magnetic Structure x=0.5x=0.4 0.4 < x < 0.5 intermediate JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999)

20. Calculated phase diagram Dima Efremov, JvdB, Daniel Khomskii, Nature Mat. (2004) Continous transition from Site centered CO Bond centered CO to “In between” centered CO Breaking of inversion symmetry in the intermediate phase Ferro-electricityMagnetism

21. Prediction for manganites: Multiferroic phase appears close to x=1/2 Conclusions Between bond- and site-centered charge order: ferroelectric phase

22. Calculated magnetic structure From: To: We find a continous transition as function of doping x=0.4x=0.5

23. Crystal field splitting of e g levelsJahn-Teller distortion Lifting of degeneracy: lattice 5x 3x 2x egeg t 2g 5x 3x 2x egeg t 2g

24. x=0.5 : Site-centered charge ordering JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999); PRL 82, 1016 (1999)

25. Goodenough (1963) Orbital order in plane Orbital order LaMnO 3 Order by disorder