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Magnetoelectric Multiferroics History and fundamentals Single-phase multiferroics Composite multiferroics Experimental techniques Summary, Literature Kathrin Drr, IFW Dresden, Postfach 270116, 01171 Dresden, Germany ESM 2007, Cluj-Napoca,

  1. Magnetoelectric Multiferroics History and fundamentals Single-phase multiferroics Composite multiferroics Experimental techniques Summary, Literature Kathrin Dörr, IFW Dresden, Postfach 270116, 01171 Dresden, Germany ESM 2007, Cluj-Napoca, 14 September 2007 Thanks to M. Fiebig 1

  2. What is a multiferroic ? “Crystals can be defined as multiferroic when two or more of the primary 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: Ferromagnetism Ferroelectricity Ferroelasticity Ferrotoroidicity spontaneous spontaneous spontaneous spontaneous magnetization polarization strain magnetic vortex + − + − + − + − + − + − N S + − + − + − + − 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 2

  3. Idea of the magnetoelectric effect 3

  4. Idea of the magnetoelectric effect 3

  5. Idea of the magnetoelectric effect magnetoelectric effect magnetic shape memory effect 3

  6. Quantification of the ME effect Free energy of magnetoelectric materials with „mixed terms“ in E , H : F(E i , H j ) = - α α i j E i H j - ½ β β ijk E i H j H k - ½ γ γ ijk E i E j H k α α β β γ γ magnetization: M(E) = - dF / dH electric polarization: P(H) = - dF / dE � requires breaking of time-reversal and space-inversion symmetries ♦ Linear magnetoelectric effect: P i = α ♦ ♦ ♦ α α ij H j ; M j = α α α α α ij E i “the“ magnetoelectric effect ♦ Higher order terms for β ♦ β ≠ 0, γ γ ≠ 0 ♦ ♦ β β γ γ 4

  7. History 1894 P. Curie: discussed correlation of "C'est la magnetic and electric properties in low- dissymmétrie symmetry crystals qui crée le 1926 P. Debye: “magneto-elektrischer phénomène" Richteffekt“ (P. Curie, 1894) 1957 L. D. Landau, E. M. Lifshitz: “The magnetoelectric effect is odd with respect to time reversal and vanishes in materials without magnetic structure.“ 1959 I. E. Dzyaloshinskii: predicted the magnetoelectric effect in Cr 2 O 3 1960 D. N. Astrov: first observation in Cr 2 O 3 5

  8. History Cr 2 O 3 M ∝ ∝ ∝ α ∝ α α α E P ∝ ∝ α ∝ ∝ α α α ∗ ∗ ∗ ∗ H 6 D. N. Astrov, JETP 11, 708 (1960) V. J. Folen, PRL 6, 607 (1961)

  9. The revival 200 Since about the year 2000: 180 ♦ New materials (“designed“ 160 Publications on 140 Publications / year composites) with much larger "magnetoelectric" 120 ME effect 100 80 ♦ New theoretical approaches / 60 concepts 40 20 ♦ New experimental techniques 0 1985 1990 1995 2000 2005 2010 (neutron scattering, non-linear Year optics) 7

  10. Sources of the magnetoelectric effect e χ α α ij 2 < χ χ ii χ jj α α χ χ χ χ Limitation of the magnetoelectric effect: m � χ ii χ χ jj χ χ χ χ χ e : electric susceptibility m : magnetic susceptibility W. F. Brown et al., Phys. Rev. 168, 574 (1968) Large in ferroelectric and ferromagnetic samples → multiferroics � N.A. Hill, J. Phys. Chem. B 104, 6694 (2000) + − + − + − + − + − + − + − + − + − + − N S “Likes“ 3d n with n=0 “Likes“ 3d n with n ≠ ≠ 0 ≠ ≠ There are very few magnetic ferroelectrics. (N. Hill alias Nicola Spaldin) 8

  11. Magnetoelectric Multiferroics History and fundamentals Single-phase multiferroics Composite multiferroics Experimental techniques Summary, Literature

  12. Single-phase multiferroics: overview • Perovskite type: Multiferroics “unusual“ ABO 3 , A 2 B`B``O 6 (e. g., BiFeO 3 , TbMnO 3 ) because they circumvent the • Hexagonal structure: d 0 / d n problem [1] RMnO 3 with R = Sc, Y, Ho-Lu • Boracites: M 3 B 7 O 13 X with M = Cr, Mn, Fe ...; X = Cl, Br, I Most are anti-ferroic in one of • Orthorhombic BaMF 4 compounds the orders (magnetic / electric) M = Mg, Mn, Fe, Co, Ni, Zn → small magnitude of M or P → → → and further ones (about 100) Very rare: RT multiferroics • Non-multiferroic magnetoelectrics: (BiFeO3: ferroelectric + antif.mag) GdFeO 3 , LuFe 2 O 4 [1] C. Ederer and N. A. Spaldin, Curr. Opin. Sol. Stat. Mat. Sci. 9, 128 (05) 9

  13. Magnetic control of ferroelectricity: TbMnO 3 ferroelectric P changes direction in large magnetic field T. Kimura et al., Nature 426, 55 (2003) 10

  14. Spin spirals as source of polarization In TbMnO 3 , a spiral spin structure and ferroelectricity appear at T ≤ T lock . � Spin spirals break time and space inversion symmetry (promising for ME effect) Polarization P ∝ ∝ ∝ e ij x (S i x S j ) proposed (H. Katsura) ∝ S i S j S i , S j : magnetic moments e ij : unit vector connecting e ij sites i, j P : polarization j s : “spin current“ H. Katsura et al., PRL 95, 057205 (2005) 11

  15. Spin spirals as source of polarization A spin spiral can be characte- rized by the propagation vector k, the rotation plane (j S ) and the cone angle β . P Note: not all spirals cause polarization ! k Neutron diffraction: determine spin spiral structure H. Katsura et al., PRL 95, 057205 (2005) 11a

  16. Charge-ordered compounds Transition metal oxides (e. g. Pr 1-x Ca x MnO 3 ): e g electrons order in insulating phases (a) Mn4+ order or (b) electron hole at the O ? � Intermediate case (c) with a) “site- b) “bond- c) broken space centered“ centered“ intermediate inversion symmetry D. V. Efremov et al., Nature Mat. 3, 853 (04) 12

  17. HoMnO 3 E E Ho 3+ Mn 3+ hexagonal structure O 2- a a P6 3 cm P6 3 cm ferroelectric at ~870 K T < T N : P6 3 cm Mn( ): antiferromagnetic, 4b 4b T N = 76 K, T SR = 34 – 40 K Ho ( ): antiferromagnetic, 2a 2a order sets in at T SR , full order at T Ho = 6 K T < T SR : P6 3 cm T. Lottermoser, M. Fiebig et al., Nature 430, 541 (2004) 13

  18. HoMnO 3 : magnetic phase control by electric field � Mn and Ho magnetic structures are coupled. � In electric field, Mn reorients and Ho becomes ferromagnetic. E ~ 100 kV cm -1 Temperature (K) 0 10 20 30 40 50 60 70 80 E E a T R SH intensity I SH Mn I SH (y) E = 0 I SH (x) b b P6 3 cm P6 3 cm I SH (y) Ho T E ≠ 0 × 1.5 T N I SH (x) 0 / µ m) 1.0 b c ) ∆Φ = [ Φ ( + E) − Φ ( − E)]/2 (° 3 Faraday rotation Φ (° Ho 0.5 2 0.0 E ≠ 0 1 E = 0 -0.5 µ 0 H z = 0.5 T 0 T = 1.4 K -1.0 -2 -1 0 1 2 0 20 40 60 80 100 T. Lottermoser, M. Fiebig et al., Magnetic field µ 0 H z (T) Temperature (K) Nature 430, 541 (2004) 14

  19. BiFeO 3 Magnetic • perovskite type structure (PEEM) • multiferroic with the highest ordering temperatures : ferroelectric: T C = 1103 K antiferromagnetic: T N = 643 K Electric (spin spiral) (PFM) Switching of FE domains (PFM tip) ⇒ switching of AFM domains in BiFeO 3 films at 300 K � Application: control the exchange bias by electric field T. Zhao et al., Nature Mat. 5 (06) 15

  20. “Electromagnons“ In magnetoelectrics, new excitations / quasiparticles are possible: Magnons (spin waves) associated with ε 1 dielectric polarization excited by GHz electric field ⇒ “electromagnons“ Resonances in the dielectric function, suppressed by magnetic field ν (cm -1 ) 30 0 A. Pimenov et al., Nature Physics 2, 97 (06) 16

  21. “Electromagnons“ In magnetoelectrics, new excitations / quasiparticles are possible: ε 2 Magnons (spin waves) associated with dielectric polarization excited by GHz electric field ⇒ “electromagnons“ Resonances in the dielectric function, suppressed by magnetic field A. Pimenov et al., Nature Physics 2, 97 (06) 16

  22. Magnetoelectric Multiferroics History and fundamentals Single-phase multiferroics Composite multiferroics Experimental techniques Summary, Literature

  23. Composite multiferroics � create large response M(E) or P(H) at ambient temperatures ferroelectric: E → → → P → Couple them and expect: + H → → P, E → → → → M → → ferromagnet: H → → M → → Magnets Ferroelectrics Tb 1-x Dy x Fe 2 BaTiO 3 multiferroic La 0.7 Sr 0.3 MnO 3 Pb(Zr,Ti)O 3 composites CoFe 2 O 4 SrBi 2 Ta 2 O 9 YIG (garnets) PMN-PT Fe, Py, .. PVDF, … 17

  24. Magnetoelectric coupling 1. Mechanical strain σ σ σ σ magnetostrictive piezoelectric H E S. X. Dong, D. Viehland et al., APL 85 (04) 2. Interface charge / bonding effects a) Field effect - - - P FE E magnet + + + E b) Bond effect: change in bonding upon P reversal alters interface magnetization C. G. Duan, E. Y. Tsymbal, PRL 95 (06) 18

  25. Types of strain-coupled composites • Mixed, sintered powders • Free-standing laminar composites • Layered thin film structures • Nanostructured composite films 20

  26. Free-standing laminar composites Piezoelectric and magnetostrictive components glued or hot-pressed together Example: PZT/Terfenol-D trilayer magnetoelectric voltage coefficient: dE/dH = 4.7 V / (cm Oe) J. Ryu et al., Jap. J. Appl. Phys. 40, 4948 (2001) 21

  27. Free-standing laminar composites Piezoelectric and magnetostrictive components glued or hot-pressed together Huge values at resonances in the AC magnetic field Sensitive (low noise) magnetic field sensors (D. Viehland et al.) J. Zhai, D. Viehland et al., APL 89, 83507 (06) 21

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