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Mul)ferroics
Dr. Tanmoy Mai) MSE 689
Acknowledgement
Some lecture slides are borrowed from
Dr. Daniel Khomskii : APS fellow, A famous Russian physicist -‐-‐ currently in Cologne University, Germany
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Ferroics
Ferroelectric materials possess a spontaneous polarization that is stable and can be switched hysteretically by an applied electric field; antiferroelectric materials possess ordered dipole moments that cancel each other completely within each crystallographic unit cell.
Ferromagnetic materials possess a spontaneous magnetization that is stable and can be switched hysteretically by an applied magnetic field; antiferromagnetic materials possess ordered magnetic moments that cancel each other completely within each magnetic unit cell.
There are three types of primary ferroics:!
Ferroelastic materials display a spontaneous deformation that is stable and can be switched hysteretically by an applied stress.
Dr. Tanmoy Mai)
• Multifunctional Material possess multiple order parameters!• Multiferroic Materials possess two or more of the following!
• (Anti-)Ferromagnetism, (Anti-)Ferroelectricity, !! (Anti-)Ferroelasticity!
Introduction to Multiferroics !
Before applied field
During and aHer applied
field
field
• Coupling between order parameters!
Hσ
M
P
ε
Magnetoelasticity!
χE
χM S
dE
α
E
dM
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Dr. Tanmoy Mai)
The combina,on of magne,c proper,es with dielectric, semiconduc,ng, or ferroelectric materials allows for the design of materials with novel func,onali,es and provides the basis for various device applica,ons. In the same material (e.g. magne,c semiconductors (MS) or intrinsic mul,ferroics) In ar,ficial heterostructures (e.g. ferromagne,c/dielectr ic heterostructures for magne,c tunnel junc,ons (MTJs) or ar,ficial mul,ferroic heterostructures)
An obvious approach for the realization of oxide materials with improved functionality is the integration of two properties in one and the same material.!
Dr. Tanmoy Mai)
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Dr. Tanmoy Mai)
but the real beginning of this field started in 1959 with a short
remark by Landau and Lifshitz in a volume of their Course of Theore)cal Physics:
“Let us point out two more phenomena, which, in principle, could exist. One is piezomagne)sm, which consists of linear coupling between a magne)c field in a so l id and a deforma)on (ana logous to piezoelectricity). The other is a linear coupling between magne)c and electric fields in a media, which would cause, for example, a magne)za)on propor)onal to an electric field. Both these phenomena could exist for certain classes of magnetocrystalline symmetry.”
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Hysterisis Loop!
Ferromagnetism.! Display spontaneous
magnetization." Produce Hysterisis Loop." Can be found mainly in metals."
Ferroelectricity.! Display spontaneous
polarization." Produce Hysterisis Loop." Ferroelectrics are insulators"
H, E
Dr. Tanmoy Mai)
Ferro-‐electric/magne)c
Multiferroics Electric and magnetic ordering in solids are usually
considered separately: effects such as ferroelectricity are caused by charges while magnetism is caused by Spins.
However, in a few cases these two orders are strongly coupled. If this is the case, then it may occur that using an electric field E, we can induce a finite magnetization M. Or using a magnetic field H, we can generate a finite electric polarization P.
If a material has both orders, namely nonzero P and M, using H we could control P or using E we can control M.
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Dr. Tanmoy Mai)
Reviews
• Sang Cheong and Maxim Mostovoy, MulFferroics: a magneFc twist for ferroelectricity, Nature Materials 6, 13 (2007).
• R. Ramesh and Nicola Spaldin, MulFferroics: progress and prospects in thin films, Nature Materials 6, 21 (2007).
• D. Khomskii, Physics 2, 20 (2009).
• Special issue of Journal of Physics: Condensed Ma`er, vol 20, number 43, 29 Oct 2008.
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Induction of magnetization by an electric field; induction of polarization by a magnetic field.
- first presumed to exist by Pierre Curie in 1894 on the basis of symmetry considerations
However, the effects are typically too small to be useful in applications!
Magnetoelectric effect
Materials exhibiting ME effect: Cr2O3 BiMnO3 BiFeO3 …..
M. Fiebig, J. Phys. D: Appl. Phys 38, R123 (2005)
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Magnetoelectric Multiferroics Materials!Cr2O3 !
• Prototypical ME, first discovered!
• P and M are field induced!
• αZZ = 4.13 ps m-1 @ E = 106 V!
• Corresponds to the magnetization observed after reversal of only 5 of every 106 spins in the AFM lattice!!!
Other ME Materials!
• Ti2O3!
• GaFeO3!
• Boracites and Phosphates!
• PbFe0.5Nb0.5O3!
• Garnet films!
• ~80 total materials have ME effects!
Top Performers !
• LiCoPO4 (αYX = 30.6 ps m-1)!
• Y3Fe5O12 films (α ~ 30 ps m-1)!
• TbPO4 (αAA = 36.7 ps m-1)!
! Principal weakness of ME Effect Perturbative nature of the microscopic
mechanisms driving ME behavior!
and ME response is limited by!
αij2 < χii
e χjjm!
Where χiie and χjj
m are the electrical and magnetic susceptibilities!
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(Ferro)magnetism vs. (Ferro)electricity Perovskite structure
(La,Sr)MnO3: spins from : 3d3 or 3d4
BaTiO3: polarization from cation/anion paired diploes
O-2
Ti+4
Magnetic moment:
- Ba+2
0.10 Å
0.05 Å 0.04 Å
+
+ Ti 3d0 O 2p2
unfilled d bands impurities
inversion symmetry broken Dr. Tanmoy Mai)
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• BiMnO3, BiFeO3, Pb(Fe2/3W1/3)O3:
6s2 lone pairs off-center distortion polar behavior
Mechanism of ferroelectricity
• PbTiO3: Pb-O covalent bond
cubic 800 K
tetragonal 300 K
Pb-O plane Ti-O plane
Pb
O
Kuroiwa et al, PRL87 217601 (2001)
Dr. Tanmoy Mai)
Materials compa)bility
FE: d0
Pb(Ti, Zr)O3 (PZT) Covalent bonding between d0 and O. This mechanism is not compa)ble with magne)sm
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Dr. Tanmoy Mai)
1.
2.
3.
4.
5.
How to combine magne,sm and ferroelectricity: Different types of mul,ferroics
In charge ordered systems, the coexistence of inequivalent sites with different charges, and inequivalent (long and short) bonds, leads to ferroelectricity.
e.g. Ni-‐I boracite (Ni3B7O13I)
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6.
7.
How to combine magne,sm and ferroelectricity: Different types of mul,ferroics
There are two types of multiferroics:
(1) Proper (or type I) multiferroics. In these cases the two phenomena of P and M occur for different reasons, but there is still a (weak) coupling between them. A famous example is BiFeO3, with TFE=1100K and TAF=643K.
(2) Improper (or type II) multiferroics. New developments. Here both orders are deeply coupled to one another. But unfortunately critical temperatures are small. In spite of this problem for applications, they are the most interesting intellectually.
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“Type I” vs. “Type II” MF BiFeO3
TbMn2O5
The magne,c and the “polar” site are dis,nct – 2 different mechanisms for FE&FM. TFE>>TC/TN>RT, but the coupling is very weak, usually through magneto-‐stric)on.
The polarisa)on is generated by the magne,c ordering. dis)nct. Weak FE and RT >TFE=TN, but the coupling is very large (“Colossal” effects).
Phys. Rev. Le`. 94, 117203 (2005)
Magneto-‐Electric coupling
Linear Magnetoelectrics (Cr2O3)
P
H
P M/Ms
TE TC/TN
“Type I” mul,ferroics (YMnO3)
P Ms
TN=TE
“Type II” mul,ferroics (TbMnO3)
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“Type II” Mul)ferroics
P Ms
TN=TE
1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm
Common Ingredient: PG symmetry must be lowered to one of the 10 pyroelectric groups.
Mul)ferroic Materials
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“Type I” Mul)ferroics
P M/Ms
TE TC/TN
Fe
Bi
(001)
AFM Ordering
FE Ordering
Polariza,on points in one of 8 possible <111> direc,ons.
Magne,c plane is perpendicular to the polariza,on direc,on.
P
Bi
Fe
O
M
M
BiFeO3 : only room temp multiferroic!
TC ~ 1103K TN ~ 643K
Bulk
Ederer and Spaldin, PRB 71(2005)
G-‐type an)ferromagnet
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A-‐type: The intra-‐plane coupling is ferromagne?c while inter-‐plane coupling is an?ferromagne?c.
C-‐type: The intra-‐plane coupling is an?ferromagne?c while inter-‐plane coupling is ferromagne?c.
G-‐type: Both intra-‐plane and inter-‐plane coupling are an?ferromagne?c.
Expected magnetic behavior!
P <111>
-‐110
-‐211
-‐101
-‐12-‐1
01-‐1 11-‐2
x y
z
P
P P
Ferroelectric domain
Easy Magne,c Axis
AFM domain
Might there be a preferred axis?
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Electrical Control!P1
+ Bi
Fe
O
* F. Kubel, H. Schmid, Acta Cryst. B46, 698 (1990)
E
P1-
P4-
109° P3-
8 possible polarization variants
3 types (180°, 71° and 109°) of ferroelectric polarization
switching
T. Zhao, M. Barry et al., Nat Mat 5, 823 (2006)
BiFeO3 SrRuO3 SrTiO3
C. Ederer and N. A. Spaldin, PRB 71, 060401(2005)
BiFeO3
TC = 1,100 K TN= 640 K.
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Geometric ferroelectrics: hexagonal RMnO3
BaNi(Mn,Co,Fe)F4 For example: YMnO3: A-type AF, lacking lone pairs, no chemically active bonding to produce ferroelectricity Buckling of MnO5 pyramids Symmetry allows Y-O distance change, hence displacement of Y : net polarization
Origin of ferroelectricity
van Aken et al., Nature Materials 3, 164, (2004)
Y
MnO5
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Site-centered charge order
• Electronic ferroelectrics: Combination of bond-centered and site-centered charge order
Efremov et al., Nature Materials 3, 853, (2004)
Bond-centered charge order Ferroelectric
intermediate state
O
TM
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Recent Discoveries
• Frustrated magnetic systems. • The magnetic phases are complicated; incommensurate AF orders seem to be common. • Strong coupling between ferroelectricty and magnetism.
TbMnO3, Nature 426, 55, (2003); PRL 95, 087206 (2005).
RMn2O5, Nature 429, 392 (2004) (Tb);
PRL 96, 067601 (2006) (Y).
TbMnO3
Kimura T, et.al, Nature 426, 55 (2003). PRB 68, 060403(R) (2003).
J1
J2
J3
Orthorhombically distorted perovskite structure (space group Pbnm) the perovskite TbMnO3 does not contain 6s lone pairs, which produce a polar structure in magne)c ferroelectric perovskites BiMnO3 and BiFeO3 Mn3+ ions with occupied d orbitals
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T=35 K
T=15 K
TN=42 K
TC=27 K
TbMnO3
Kenzelmann et al., PRL 95, 087206 (2005)
IC sinusoidally modulated collinear magnetic order, inversion symmetric
IC non-collinear magnetic order, inversion symmetry broken
Long wavelength incommensurate AF spin ordering␣ coupled to lalce to produce inversion symmetry breaking
The effect of spin frustra,on causes sinusoidal an,ferromagne,c ordering. The modulated magne,c structure is accompanied by a magnetoelas,cally induced lalce modula,on, and with the emergence of a spontaneous polariza,on.
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Conclusions • Magne)c mul)ferroics are a lot more common than previously
thought! In fact, the development of a small polariza)on may be ubiquitous given an appropriate magne)c symmetry.
• Mul)ferroics are fascina)ng materials and they may even be useful… They definitely made (re)learn some very clever physics.
• More generally, mul)ferroics remind us that most interes)ng physical proper)es emerge from (point) group symmetry breaking (“Neumann” tensors).
The theory (and prac,ce) of symmetry is key to all new materials proper,es.
Exotic results already found
• The interface between two insulators can be a metal
• The interface between two insulator can be a superconductor
• In general, the properties of the ensemble can be drastically different from the properties of the individual building blocks
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nature materials VOL 7, Page 478 JUNE 2008
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Sketch of a possible MERAM element. The binary information is stored by the magnetization direction of the bottom FM layer (blue), read by the resistance of the magnetic trilayer (Rp when the magnetizations of the two FM layers are parallel), and written by applying a voltage across the multiferroic FE –AFM (green) layer . If the magnetization of the bottom FM layer is coupled to the spins in the multiferroic (small white arrows) and if the magnetoelectric coupling is strong enough, reversing the FE polarization P in the multiferroic changes the magnetic configuration in the trilayer from parallel to antiparallel, and the resistance from Rp to antiparallel (Rap).
nature materials | VOL 7 | Page 425, JUNE 2008
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