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What is known about multiferroic BiFeO 3? Perovskite: Bi A sites; FeO 6 octahedra • Rhombohedral R3c (10 atoms/cell) • [Large distortions from cubic perovskite] • Ferroelectric: Ps ~ 6 mC/cm 2 , T c ~ 1120 K • Bi 3+ (6s 2 6p 0 ), Fe 3+ (3d 5 ) states • Weak FM insulator, T AFM ~ 650 K • G-type, rock-salt spin order + spiral structure (~620 Å period) • No optical measurements available BiFeO 3 Bi 3+ O 2- • Kubel & Schmid (1991), Teague et al (1970), Sosnowska et al (1982). 3.96 Å Fe 3+ (d 5 )
C. Michel et al, Solid State Communications, 1969 Properties of Bulk BiFeO 3 Bi: 0.62Å along (111) Fe: 0.23Å along (111) O: 0.30Å rotating about (111) Spontaneous Polarization Ps=6.2µC/cm 2 , Ec=20kV/cm Measured at liquid nitrogen T J. R. Teague, et al. Solid State Communications, 8, 1970
Page 1 and 2: Functional Materials II: Ferroics a
Page 3 and 4: Ferroics and Multiferroics • Smar
Page 5 and 6: Ferroelastic Material Strain T Eg.
Page 7 and 8: Symmetry Properties: Ferroics The f
Page 9 and 10: Symmetry Properties: Ferroics Symme
Page 11 and 12: Ferroelectric BaTiO 3 Ba Ti O High
Page 13 and 14: (1) Polarization Tetragonal Tempera
Page 15 and 16: Why PZT is one of the best ferroele
Page 17 and 18: K α (T-T c) L α (T-T c) 1/2 Diele
Page 19 and 20: Unifying Concept[s] in Materials
Page 21 and 22: Born-Oppenheimer Approximation If I
Page 23 and 24: Energy Function: E total(d i, Z i)=
Page 25 and 26: Generalized Landau Theory: a real f
Page 27 and 28: Order of Phase Transition C6>0 C2>0
Page 29 and 30: Domain wall energies of Ferroelectr
Page 31 and 32: INTRODUCTION (out of 122)
Page 34 and 35: Tetragonal PbTiO 3 & BaTiO 3 Ti Z*x
Page 36 and 37: Mechanisms in multiferroic ((A)FM+F
Page 38 and 39: Chemical origin of FE in BiFeO 3 Wa
Page 40 and 41: InMnO 3, YMnO 3: Improper ferroelec
Page 42 and 43: InMnO 3 • P=19 µC/cm 2 (as obtai
Page 44 and 45: InMnO 3: Response to Strain Main st
Page 46 and 47: Fe 3+ LuFe 2O 4 Fe 2+ Charge Orderi
Page 50 and 51: Metallic nonmagnetic & ferromagneti
Page 52 and 53: Rotation about the [111] axis opens
Page 54 and 55: Perovskite design by epitaxy • Ar
Page 56 and 57: Polarization (uC/cm2) 80 60 40 20 0
Page 58 and 59: Tetragonal P4mm (P s || [001]) LSDA
Page 60 and 61: Chemical origin of FE in BiFeO 3 Wa
Page 62 and 63: First-principles Determination of S
Page 64 and 65: Electron Density of States: YCrO 3
Page 66 and 67: YCrO 3: interaction between Y and O
Page 68 and 69: Oxygen Vacancies in BaTiO 3 Mangala
Page 70 and 71: M (emu/g) 4.0x10 -4 3.0x10 -4 2.0x1
Page 72 and 73: 0 % 12 9 6 3 1 kHz 10 kHz 100 kHz 1
Page 74 and 75: Hunds’ coupling stabilizes FM sta
Page 76 and 77: Opposite example: BaFeO 3-δ See Po
Page 78 and 79: La 2NiMnO 6 78
Page 80 and 81: La 2NiMnO 6: a ferromagnetic insula
Page 82 and 83: FiM Soft IR-active modes upon chang
Page 84: SUMMARY • Interesting Physics of

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