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