First-principles study of spontaneous polarization in
multiferroic BiFeO3
Yoshida lab.
Ryota Omichi
2014.05.28
PHYSICAL REVIEW B 71, 014113 (2005)
Contents
• Introduction• Multiferroic • Electric polarization• Properties of BiFeO3
• Calculation methods(LDA and LDA+U)• Results
• Electronic structure• Spontaneous polarization
• Summary• Future works
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
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
+ +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
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)
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
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)
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
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
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
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
Modern theory of polarization
Polarization quantum
• Physical quantity resulting from uncertainty of phase
(In the case of Ueff=0)
Polarization
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
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 .
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