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Ferroelectrics to Magnetoelectrics&Multiferroics

Ferroelectrics to Magnetoelectrics&Multiferroics. Ferroelectrics (Valasek,1920’s): Spontaneous electric polarization ( P ), e.g., BaTiO 3 (displacive) & NaNO 2 (order – disorder). Proper FE: P as OP drives structural phase transition at T C ; C-W law of dielectric constant ε (T).

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Ferroelectrics to Magnetoelectrics&Multiferroics

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  1. Ferroelectrics to Magnetoelectrics&Multiferroics Ferroelectrics (Valasek,1920’s): Spontaneous electric polarization (P), e.g., BaTiO3 (displacive) & NaNO2 (order – disorder). Proper FE: P as OP drives structural phase transition at TC ; C-W law of dielectric constant ε(T). Improper FE: P is by-product of of another structural phase transition with different OP.

  2. Ferroelectricity in charge ordered systems Cheong & Mostovoy, NM(2007) Site-centered/bond-centered Exchange striction Charge transfer Charge & spin ↑↑↓↓ order

  3. Field Description: E  P, H  M; σ  ε Recent(1990’s)resurgence of interest{exp.&theo.} Magnetoelectrics (late 1950’s-theory; early 1960’s-experiment) Multiferroic Materials (Cologne work) Fundamental Physics of Multiferroics Fundamental Physics vs. Applied Physics Engineering  Devices Magnetoelectrics and Multiferroics

  4. Idea of the Magnetoelectric Effect Electric field Mechanical stress Magnetric field

  5. Idea of the Magnetoelectric Effect Polarization Mech. Strain Magneti- zation

  6. Idea of the Magnetoelectric Effect

  7. Idea of the Magnetoelectric Effect Magnetoelectric Effect

  8. Magnetoelectric Effect: Historical SurveyTheoretical driven, then experimentally observed • 1894— First discussion of an intrinsic correlation between magnetic and electric properties • P. Curie, J. de Physique (3rd Series) 3, 393 (1894) • "Les conditions de symétrie nos permettons d'imaginer qu'un corps à molécule dissymétrique se polarise peut-être magnétiquement lorsqu'on le place dans un champ électrique. • 1926— Introduction of the term "magnetoelectric" for these correlations • P. Debye, Z. Phys. 36, 300 (1926) • Title: Bemerkung zu einigen neuen Versuchen über einen magneto-elektrischen Richteffekt • 1957— Magnetoelectric effect only in time-asymmetric (i.e. magnetically ordered) media! • L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960) • "The magnetoelectric effect is odd with respect to time reversal and vanishes in materials without magnetic structure" • 1959— Magnetoelectric effect predicted for antiferromagnetic Cr2O3 • I. E. Dzyaloshinskii, J. Exptl. Teor. Fiz. 37, 881 (1959); Sov. Phys.—JETP10, 628 (1959) • "We should like to show here that among the well known antiferromagnetic substances there is one, namely Cr2O3, where the magnetoelectric effect should occur from symmetry considerations." • 1960/61— First observation in Cr2O3 • E  M:D. N. Astrov, J. Exptl. Teor. Fiz. 38, 984 (1960); Sov. Phys.—JETP 11, 708 (1960) • H  P:V. J. Folen, G. T. Rado, and E. W. Stalder, Phys. Rev. Lett. 6, 607 (1961)

  9. Magnetoelectric Effect: Historical Survey 1960: MaE "C'est la dissymmétrie qui crée le phénomène" (P. Curie, 1894) Cr2O3 V.J. Folen, PRL 6, 607 (1961) D.N. Astrov, JETP 11, 708 (1960) 1961: Pa*H • 1960: • Theoreticallynotwellunderstood • Small effect (10-5) • Limited choice of compounds 2000: • New theoretical concepts • "Giant" effects: induction of phase transitions • New materials: "magnetoelectricity on design" Review: J. Phys. D 38, R123 (2005)

  10. Limitation of the magnetoelectric effect: Cannot be larger than the geometric mean of electric and magnetic permeability [W. F. Brown, R. M. Hornreich, S. Shtrikman, Phys. Rev.168, 574 (1968)] aij2 < ciiecjjm Generating Large Magnetoelectric Effects Large magnetoelectric effects: • In ferroelectric samples • In ferromagnetic samples Largest: in ferroelectric ferromagnetics Do ferroelectric ferromagnetics exist? Yes!! They are called multiferroics!

  11. + + + - - - + + + - - - + + + - - - + - N S What is a “Multiferroic”? “Crystals can be defined as multiferroic when two or more of the xprimary ferroic properties are united in the same phase.” Hans Schmid (University of Geneva, Switzerland) in: M. Fiebig et al. (ed.), Magnetoelectric Interaction Phenomena in Crystals, (Kluwer, Dordrecht, 2004) Excludes anti-ferroic forms of ordering Primary ferroic  formation of switchable domains: FerromagnetismFerroelectricityFerroelasticityFerrotoroidicity spontaneous spontaneous spontaneous spontaneous magnetization polarization strain magnetic vortex Extension to anti-ferroic forms of ordering: Compounds consisting of multiferroic sublattices (one or more of) whose primary ferroic properties cancel in the macroscopic crystal

  12. layered particulate 1 1: piezoelectric 2: magnetostrictive 2 What is a Composite Multiferroic? Constituent 1: Piezoelectric BaTiO3 PbZr1-xTixO3 (PZT) Ba0.8Pb0.2TiO3 Bi4Ti3O12 PVDF PbMg1/3V2/3O3 ... Constituent 2: Magnetostrictive CoFe2O4 Tb1-xDyxFe2 (= Terfenol-D) LiFe5O8 YIG Permendur ... • Composite • Pseudo-magnetoelectric • End compounds are not magnetoelectric! • Magnetoelectric effect is a product effect!   • Magnetic field  magnetostrictive deformation • Transfer of deformation constituent 2  constituent 1 • Deformation via piezoelectric effect  voltage

  13. First Composite Magnetoelectric Effect Result: Value of the magnetoelectric pseudo effect in BaTiO3/CoFe2O4: dE/dH = 130 mV/cmOe a = 720 pT/Vm-1 Compare to best single-phase magnetoelectrics: Cr2O3: a = 4.13 pT/Vm-1 TbPO4: a = 36.7 pT/Vm-1 No significant advances on this initial result until the year 2000! BaTiO3/CoFe2O4

  14. H0 H(w) ~10 kOe ~10 Oe w = 100 Hz – 1 MHz 0 0 0 0 Time Time Vmax,w Hmax,w Measuring Magnetoelectric Response in Composites V(w) Hmax,w V =101...5 mV/cmOe 0 0 Time • The composite ME effect is an AC effect • Linear response for small intervals only G. Srinivasan et al., Phys. Rev. B 67, 014418 (2003)

  15. Self-Assembled Nanocomposite Multiferroics Ferroelectric properties Ferromagnetic CoFe2O4 pillars Ferroelectric BaTiO3 matrix Ferromagnetic properties SrTiO3 substrate ME coupling and phase control also observed ! H. Zheng et al., Science 303, 661 (2004)

  16. Magnetoelectric Phase Control in Nanocomposites Force microscopy on BiFeO3/CoFe2O4 Magnetic control by electric field - + 1 mm Magnetic +20 kOe Magnetic -20 kOe Electric 8 V MFM before MFM afterapplication of +12 V ME coupling mediated by strain Estimated: (10 V/cmOe)-1 Line scans of marked regions F. Zavaliche et al., Nano Lett. 5, 1793 (2005)

  17. Natural Single-Phase Multiferroics Three natural crystals Congolite Fe3B7O13Cl Hubnerite MnWO4 Chambersite Mn3B7O13Cl See Cologne work

  18. Ni3B7O13I – A Milestone of Multiferroics Research E. Ascher, H. Schmid et al., J. Appl. Phys. 37, 1404 (1966) • Rotation of magnetization by 90° [110]  [110] • Triggers reversal of ferroelectric polarization [001]  [001] • First example of magnetoelectric cross-control

  19. Mn3B7O13I TbMn2O5 + + + - - - + + + - - - + + + - - - + - O. Crottaz, Ferroelectrics 204, 45 (1997) N S Ferroelectric Ferromagnets Most promising for applications, but not many compounds exist because... Likes 3dn with n=0 Likes 3dn with n0 N.A. Hill, J. Phys. Chem. B 104, 6694 (2000) The existing ferroelectric ferroelectrics are usually anti-ferroic with only a weak ferromagnetic or ferroelectric component: N. Hur, Nature 429, 392 (2004) Thequestfor strongferroelectricferromagnetsat300Kisstillfarfrombeingsolved!

  20. Magnetic Control of Ferroelectricity in TbMnO3 See Cologne work Magnetically driven ferroelectricity Magnetic field triggers a ferroelectric phase transition with polarization rotation by 90° T. Kimura et al., Nature 426, 55 (2003)

  21. Magnetic Phase Control by Electric Field in HoMnO3 T. Lottermoser et al., Nature 430, 541 (2004)

  22. Theory of Multiferroics in Magnetic Spirals • (P,E) and (M,H) linear coupling when they vary both in space and time: ∂E/∂r ≈ ∂H/∂t • Seek non-linear coupling, e.g., inhomogeneous magnetic order: third order coupling PM∂M, then magnetically induced electric polarization • So must search for spiral magnetic order, e.g., TbMnO3 et al. • Spiral states are characterized by two vectors: Q propagation vector and e3 = e1 x e2 , spin rotation axis. Therefore for non-collinear magnets: P ║ e3x Q

  23. Magnetic Tunabilityof Multiferroics

  24. How to measure P and ε?HW problems

  25. Symmetry Breakings Required for Multiferroics Magnetic order breaks time reversal symmetry(TRS) Displacements of O2- breaks inversion symmetry (ISB) Magnetic exchange interaction (with order - TRSB) causes displacement of Mn3+ - ISB

  26. Cologne Work on Multiferroics – Pyroxenes (AMSi2O6)

  27. Pyroxenes :NaFeSi2O6, LiFeSi2O6 and LiCrFe2Si6 natural mineral (crystal aegirine)

  28. Magnetic properties of NaFeSi2O6

  29. Dielectric properties of NaFeSi2O6 How can you measure the electrical polarization ?

  30. Anisotropy of Polarization Pb and Pc

  31. Phase diagram of NaFeSi2O6

  32. Questions Comments Suggestions ? Future Ideas ? Magnetoelectrics and Multiferroics – The End

  33. Pyrocurrent measurements of MnWO7

  34. Cologne Work – TbMnO3

  35. Thermal Expansion and Magnetostriction

  36. Thermal Conductivity and Thermal Expansion

  37. GdMnO3 – Thermal Expansion and Magnetostriction

  38. Ferroelectrics  Multiferroics

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