1. Jeroen van den Brink LaOFeAs -- multiferroic manganites Krakaw 19/6/2008 Gianluca Giovannetti,Luuk Ament,Igor Pikovski,Sanjeev Kumar,Antoine Klauser,Carmine Ortix George Sawatzky,Frank Kruger,Ilya Elfimov,Jan Zaanen

2. Layered crystal structure LaOFeAs Fe d 6 tetrahedral surrounding egeg t 2g egeg S=2S=1S=0 exp. ordered moment: 0.4  B (bad) metal C-type magnetic order

3. Giovannetti, Kumar, JvdB, arXiv:0804.0866 Phys B. doi:10.1016 (2008) LaOFeAs: LDA+U, C-type magnetic order Fe 3d-band width ~4 eV S=2 gap ~0.5 eV

4. Stochiometric LaOFeAs S=2, Mott insulator Experimental small moment and “metallicity” are due to off-stochiometry high spin Fe found in XAS Bernd Buchner, Martin Knupfer arXiv:0806.2625 Giovannetti, Kumar, JvdB, Phys B. doi:10.1016 (2008)

5. Multiferroics = Magnetic Ferroelectrics Why study them?Magnetic ferroelectrics are very rare! Fundamental interest: Why rare? How to get around? How to get strong coupling between magnetic and ferroelectric orderparameter? Van Aken et al., Nature 449, 702 (2007) Cheong and Mostovoy, Nature Mat. 6, 13 (2007) Eerenstein et al., Nature 442, 759 (2006) Pimenov et al., Nature Phys. 97, 100 (2006) Ikeda et al., Nature 436, 1136 (2005) Lottermoser et al., Nature 430, 541 (2004) Zheng et al., Science 303, 661 (2004) Kimura et al., Nature 426, 55 (2003) Hur et al., Nature 429, 392 (2003)

6. Observed multiferroic couplings -- BiFeO 3 and BiMnO 3 T magnetic <<T ferroelectric orderparameters barely couple -- Pr 1-x Ca x MnO 3, HoMn 2 O 5 magnetism induces FE, but: no chiral symmetry breaking -- TbMnO 3, DyMnO 3, Ni 3 V 2 O 8 T ferroelectric =T magnetic magnetism induces FE chiral magnetic order (spin spiral) does the job Maxim Mostovoy, PRL 96, 067601 (2006) ???

7. Mn 3+ Mn 4+ HoMn 2 O 5 Mn 3+ Mn 4+

8. HoMn 2 O 5 Mn 3+ Mn 4+ +-+-+- displacements due to dislocated SDW / magneto-striction electronic and ionic ferroelectric polarization conceptual picture Betouras, Giovannetti, JvdB, PRL 98, 257601 (2007)

9. Ab initio bandstructure computations ~1200 nC/cm 2 Incorporating electron correlation effects with LDA+U fixes the problem experimental polarization ~80 nC/cm 2 ferroelectric domains?

10. small polarization due to near cancellation of P ion and P elec Gianluca Giovannetti and JvdB, PRL 100, 227603 (2008)

11. 11 Mn 4+ / Mn 3+ Oxygen 2- Pr 3+ /Ca 2+ Perovskite crystal structure of Pr 1-x Ca x MnO 3 0.4 < x < 0.5

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

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

14. Ferroelectric? x=0.5x=0.4 Site centered spin/CO Bond centered spin/CO Ferro-electric groundstate 0.4 < x < 0.5 intermediate It is allowed by symmetry:can happenwill happen Jooss et al., PNAS 104, 13597 (2007) observed to happen

15. ....and it first happened in microscopic DDEX model JvdB, Khomskii, PRL 82, 1016 (1999) Efremov, JvdB, Khomskii, Nature Mat. (2004) stabilization of dislocated SDW phasemultiferroicity

16. Continous transition from Site centered CO Bond centered CO to “in between order” Computed phase diagram of Pr 1-x Ca x MnO 3 Efremov, JvdB, Khomskii, Nature Mat. (2004) Breaking of inversion symmetry in the intermediate phase Ferro-electricityMagnetism

17. Giovannetti, Kumar, JvdB, Picozzi, preprint (2008)

19. we predict.... LaOFeAs to be Mott insulator with Fe high spin La 1/2 Ca 1/2 MnO 3 to be strongly multiferroic Conclusions

20. Simple 1D Picture suggests FE in quasi-1D organic charge transfer salts which is observed! e.g.: S. Brazovskii, Physics of Organic Superconductors and Conductors Springer Series in Materials Sciences (2008). longitudinal charge displacements

21. Perovskite HoMnO 3 with GdFeO 3 distortion Magnetic E-phase S. Picozzi et al., Phys. Rev. Lett. 99, 227201 (2007).

22. Simple 1D Picture Superexchange strengthens bonds of antiparallel spins Double exchange strengthen bonds of parallel spins all oxygens move down! transversal charge displacements JvdB and Daniel Khomskii, J. Phys. C.M., in press (2008)

23. HoMn 2 O 5 CM+FE ICM+PE Kimura, Kamada, Noda, Kaneko, Metoki, Kohn cond-mat/0602226 (2006)

24. 1. Phenomenological approach

25. Magneto-electric coupling: Ginzburg-Landau Electric polarization Magnetization Free energy must be invariant for: time reversalspatial inversion couple these two orderparameters

26. Magneto-electric coupling: Ginzburg-Landau To build an invariant we need We are interested in ferroelectrics: uniform electric polarization so that which implies that: SPIRAL

27. Our key observation: Betouras, Giovannetti, JvdB, PRL 98, 257601 (2007) becomes active if SDW dislocated magnetization is shifted with respect to the lattice (but inversion invariant) Giovannetti and JvdB, PRL 100, 227603 (2008)

28. Minimize Free Energy with Ansatz for polarization gives finite p 0 and p 1 only when q m = q/2 For multiferroic coupling it is sufficient to have commensurate dislocated magnetic order with

29. Chapon, Radaelli, Blake, Park, Cheong Phys. Rev. Lett. 96, 097601 (2006) ICM CM ICM ICM: incommensurate magnetic ordering CM: commensurate YMn 2 O 5 indeed only commensurate magnetic phase is ferroelectric!