first-principles study of spontaneous polarization in multiferroic bifeo 3 yoshida lab. ryota omichi...
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![Page 1: First-principles study of spontaneous polarization in multiferroic BiFeO 3 Yoshida lab. Ryota Omichi 2014.05.28 PHYSICAL REVIEW B 71, 014113 (2005)](https://reader030.vdocument.in/reader030/viewer/2022032803/56649e365503460f94b26330/html5/thumbnails/1.jpg)
First-principles study of spontaneous polarization in
multiferroic BiFeO3
Yoshida lab.
Ryota Omichi
2014.05.28
PHYSICAL REVIEW B 71, 014113 (2005)
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Contents
• Introduction• Multiferroic • Electric polarization• Properties of BiFeO3
• Calculation methods(LDA and LDA+U)• Results
• Electronic structure• Spontaneous polarization
• Summary• Future works
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Intro ~multiferroic materials~
Magnetoelectric effect
N. A. Spaldin and M. Fiebig,Science 309, 391 (2005)
Ferroic :: P,M or ε are spontaneously formed to produce ferroelectricity, ferro/antiferro-magnetism or ferroelasticityMultiferroic :: co-existence of at least two kinds of ferroic orderingsMagnetoelectricity :: Control of P(M) via a magnetic(electric) field
電気磁気効果
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Intro ~ferroic quantities~
M
H
P
E
Ps
Ec
Ms
Hc
1’ 1
M -M
P P
M M
P -P
Ferroic(M and P) quantities are classified by their symmetry transformations under space and time reversal. 時間反転対称性
空間反転対称性
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+ +ー ー
+ ー
+q -q
a
para
Calculation of polarization
d (displacement)
+
+ ー +
Spontaneouspolarization
Intro ~electric polarization~
• Not available within periodic boundary conduction(depends on unit cell choice)
r :: distance of chargeq :: charge
ferro
自発分極
Electric polarization : R. D. King-Smith and David Vanderbilt, Phys. Rev. B 47, 1651(1993)
origin
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Intro ~properties of BiFeO3~
Bi
FeO
• R3c (No167) structure polarization direction [1 1 1]• Feroelectricity and antiferromagnetism• Formal charge Fe3+ Bi3+ O2-
• Ferroelectricity below 1100K (Curie temperature)• Antiferromagnetism below 600K (Neel temperature)• 6 coordinates
[1 1 1]
Super exchange interaction : P.W.Anderson, Phys. Rev. 79 350 (1950)J. Kanamori, J. Phys. Chem. Solids 10 87 (1959)
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First principles calculations
Parameter based on experiment
○ Predict physical properties of materials
Input parameter
Only atomic number and atomic position
第一原理計算
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Calculation methods• Density functional theory
• HK theory• Kohn Sham theory
• LDA method
DFT: 密度汎関数理論LDA: 局所密度近似
v
Veff( 補助場 )
DFT : P. Hohenberg and W. Kohn,Phys. Rev. 136 B864 (1964)W. Kohn and L. J. Sham, Phys. Rev. 140 A1133 (1965)
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Calculation methods
Error of LDA method
• Underestimation lattice constant and band gap• Predicting metallic behavior for materials that are
known to be insulators
Improvement plan
Introduction of Ueff(U-J)• U :: Hubberd parameter• J :: exchange interaction LDA+U :
S. L. Dudarev et. Al, Phys. Rev. B 57 1505 (1998)
LDA method
• Effective method in condensed matter
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Results ~DOS~(a) Majority spin(BiFeO3)(b) Local Fe DOS for both spin channels(c) Local Fe DOS (Ueff=2eV) gap=1.3eV(d) Local Fe DOS (Ueff=4eV) gap=1.9eVCrystal splitting
Sprit of Fe 3d states
t2g
eg
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Modern theory of polarization
• Ionic contribution• Electronic contribution
Electronic contribution
• P is calculated by using Berry phase .
Bloch function Wannier functionFourier transform
Localization of Electron
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Electric polarization and Wannier orbital
Maximally Localized Wannier Function (MLWF)
Wannier center
Polarization can be written by sum of Wannier centers
BaTiO3
py
noncentrosymmetric
centrosymmetric
Berry phase
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Modern theory of polarization
Polarization quantum
• Physical quantity resulting from uncertainty of phase
(In the case of Ueff=0)
Polarization
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Switching path
α=60° Ueff=2eVPolarization quantum = 185.6(μC/cm2)
Change in polarization P along a path from the original R3c structurethrough the centrosymmetric cubic structure
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Summary
• BiFeO3 is a materials of unusual interest both as a potentially useful multiferroic and with respect to its fundamental polarization behavior .
• Since some of the observed values of polarization can only be explained be switching structures in which the ions change their valence states , such behavior , if experimentally verified might be unique to multiferroics .
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properIonic displacement. Break inversionsymmetry (IS)
improperElectron degrees of freedom break (IS)
FERROELECTRICITY
Future works
In order to obtain a large magnetoelectronic coupling, weinvestigate improper ferroelectrics by first-priniples and modelapproaches.
Spin-order (some AFM or spiral)
HoMnO3
Spin-order (AFM)
Cu2MnSnS4