lecture vi: an introduction to modern approach of polarization...
TRANSCRIPT
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Lecture VI: An Introduction to Modern Approach of Polarization Theory
South China University of Technology
Yu-Jun Zhao
South China University of Technology
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背景-多铁体
多铁体(multiferroic)
Spaldin and Fiebig, Science 309, 391 (2005)
铁性分类
Multi:多,ferroic:含铁的,源自拉丁词汇ferrum(铁 )
Multiferroic: 具有多重铁性的材料多种极性序参量
—Hans Schmid, Ferroelectrics 162, 317 (1994)
Van Aken, Rivera, Schmid,Fiebig. Nature 449, 702 (2007)
铁弹性
铁涡性
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背景-磁电效应
电磁场耦合方程
磁电效应
电磁场内稟性质
电场(磁场) 对物质磁性(介电)性质的影响
P = αH, M =αE
应用领域
电场(磁场)传感(探测)器,转换器
电场控制的磁纪录存储
Eerenstein, Mathur and Scott, Nature 442, 759 (2006)
Wood和Austin :15种用途Int. J. Magn. 5,303(1973)
多铁体和磁电体的范畴
J. C. Maxwell
6/13/1831~11/5/1879
Phil. Trans. R. Soc. Lond. 155, 459–512 (1865)
magnetoelectric effect: P. Debye 1926 Z. Phys. 36 300
磁电耦合:表征介质磁学性质和介电性质的序参量,即磁化强度M和电极化强度P之间的耦合
磁电体自身性质
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背景-历史回顾
早期 (1888-1958)
小高潮(1958-1993)
0
50
100
150
200
250
300
350
400
1993 1995 1997 1999 2001 2003 2005 2007
ISI Statistics: keyword magnetoelectric
and multiferroic
Magnetoelectric
Multiferroic
1888年,Röntgen :处于电场中的运动介质会被磁化 (Ann. Phys. 35, 264 )1905年, H.A. Wilson,逆效应:处于磁场中的运动介质会被电极化 (Phil.Trans. R. Soc. A 204, 129)1894年,P. Curie(对称性原理):用磁场使介质电极化或者用电场使介质磁极化 J. Physique 3,393
实验努力大多失败Debye, Condon, van Vleck
1958年,Landau和Lifshitz :时间反演对称性
1959年,Dzyaloshinskii:Cr203
1960年,Astrov实验证实(JETP 11, 708)
1958年,Smolensky和Ioffe:铁电性铁磁体 Pb(Fe0.5Nb0.5)O3
复兴(1993-Present)
至1973年共有80多种磁电体被发现,随后研究进入低谷
2000年,N.A. Hill, J. Phys. Chem. B 104, 6694
1994年,C. W. Nan Phys. Rev. B 50,6082
2005年,M. Fiebig, Phys. D: Appl. Phys. 38, R123
2003年,J. Wang等:BiFeO3,Science 299, 1719
2005年以来,平均每年5篇review papers多家杂志作了专题报道Science:2008年七大科技热点
复兴原因
理论发展,实验进步,社会需求
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Electrical Polarization theory
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Electric dipole
Water Molecule
x
y
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Polarization in bulk
NaCl 离子晶体CM 模型:极矩可用局域的电荷中心来描述
Si
共价晶体
(阴影部分是外电场引起的负电荷集聚区域)
无法用电荷中心来描述(有很大一部分是键的贡献)
如果一定要用CM模型来描述的话,无论怎样取单位原胞和电荷中心,得到的高频介电常数仅为实验值(12)的~1/10.
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Dielectric Constants of Bulks
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Ferroelectric Crystals
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Issue on Polarization in bulk
2.
In order to apply it, we need to assume a macroscopic
but finite crystal. Not a bulk description.
1.
However, this approach is also flawed, because the
result depends on the shape and location of the unit cell.
From textbook of Aschcroft and Mermin
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Issue on Polarization in bulk
3. As a third approach, one might imagine defining P as the
cell average of a microscopic polarization Pmicro defined via
However, the above equation does not uniquely define Pmicro(r).
(E.g., shift a constant for Pmicro)
The periodic electronic charge distribution in a polarized
crystalline solid cannot, even in principle, be used to construct
a meaningful definition of bulk polarization.
However, this important message has not received the wide
appreciation it deserves, nor has it reached the most popular
textbooks.
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Issue Polarization in bulk
From textbook of Aschcroft and Mermin
P is a bulk property or surface property?
From Kittel’s textbook (8th ed).
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Issue Polarization in bulk
The conclusion to be drawn from the above discussion is that a
knowledge of the periodic electronic charge distribution in a
polarized crystalline solid cannot, even in principle, be used to
construct a meaningful definition of bulk polarization.
A modern approach has been developed since 1970s (significant
works were done in 90s).
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Modern Approach
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How is Induced Polarization Measured?
(介电常数)
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How is Induced Polarization Measured?
以压电效应的测量为例:
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How is Ferroelectric Polarization Measured?
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Prescription for a theory of Polarization
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Prescription for a theory of Polarization
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Berry Phase Theory
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Berry Phase Theory
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Berry Phase Theory
Berry phase
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Calculation of polarization
Berry phase
虚部
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Calculation of polarization
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The Quantum of Polarization
Berry phase 满足
所以形式电极矩(formal polarization)
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Formal polarization vs normal polarization
(形式极矩 vs 常规极矩)
A useful way to think about the presence of this “modulus”
is to regard the formal polarization as a multivalued vector
quantity, rather than a conventional single-valued one.
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Formal polarization vs normal polarization
(形式极矩 vs 常规极矩)
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References
1. Physics of ferroelectrics: a modern perspective
By Karin Maria Rabe, Charles H. Ahn, Jean-Marc Triscone
Chapters by Resta and Vanderbilt
Available at springerlink.com
2. Macroscopic polarization in crystalline dielectrics: the
geometric phase approach
R. Resta, Rev. Mod. Phys. 66, 899(1994)