Lecture schedule October 3 – 7, 2011
#1 Kondo effect #2 Spin glasses #3 Giant magnetoresistance #4 Magnetoelectrics and multiferroics #5 High temperature superconductivity #6 Applications of superconductivity #7 Heavy fermions #8 Hidden order in URu2Si2 #9 Modern experimental methods in correlated electron systems #10 Quantum phase transitions
Present basic experimental phenomena of the above topics
Ferroelectrics to Magnetoelectrics&Multiferroics
Ferroelectrics (Valasek,1920’s): Spontaneous electric polarization (P), e.g., BaTiO3
(displacive) & NaNO2 (order – disorder).
Proper FE: P as OP drives structural phase transition at TC ; C-W law of dielectric constant ε(T).
Improper FE: P is by-product of of another structural phase transition with different OP.
Ferroelectricity in charge ordered systems
Site-centered/bond-centered Exchange striction
Charge transferCharge & spin ↑↑↓↓ order
Cheong & Mostovoy, NM(2007)
Magnetoelectrics and Multiferroics
• Field Description: E P, H M; σ ε• Recent(1990’s)resurgence of interest{exp.&theo.}• Magnetoelectrics (late 1950’s-theory; early
1960’s-experiment)• Multiferroic Materials (Cologne work)• Fundamental Physics of Multiferroics• Fundamental Physics vs. Applied Physics • Engineering Devices
Idea of the Magnetoelectric Effect
Electric field
Magnetricfield
Mechanical stress
Idea of the Magnetoelectric Effect
Mech.Strain
Magneti-zation
Polarization
Idea of the Magnetoelectric Effect
Idea of the Magnetoelectric Effect
Magnetoelectric Effect
Magnetoelectric Effect: Historical Survey
Theoretical driven, then experimentally observed
1894 — First discussion of an intrinsic correlation between magnetic and electric propertiesP. Curie, J. de Physique (3rd Series) 3, 393 (1894)"Les conditions de symétrie nos permettons d'imaginer qu'un corps à molécule dissymétrique se polarise peut-être magnétiquement lorsqu'on le place dans un champ électrique.
1926 — Introduction of the term "magnetoelectric" for these correlationsP. Debye, Z. Phys. 36, 300 (1926)Title: Bemerkung zu einigen neuen Versuchen über einen magneto-elektrischen Richteffekt
1957 — Magnetoelectric effect only in time-asymmetric (i.e. magnetically ordered) media!L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)"The magnetoelectric effect is odd with respect to time reversal and vanishes in materials without magnetic structure"
1959 — Magnetoelectric effect predicted for antiferromagnetic Cr2O3
I. E. Dzyaloshinskii, J. Exptl. Teor. Fiz. 37, 881 (1959); Sov. Phys.—JETP 10, 628 (1959)"We should like to show here that among the well known antiferromagnetic substances there is one, namely Cr2O3, where the magnetoelectric effect should occur from symmetry considerations."
1960/61 — First observation in Cr2O3
E M: D. N. Astrov, J. Exptl. Teor. Fiz. 38, 984 (1960); Sov. Phys.—JETP 11, 708 (1960)H P: V. J. Folen, G. T. Rado, and E. W. Stalder, Phys. Rev. Lett. 6, 607 (1961)
Magnetoelectric Effect: Historical Survey
"C'est la dissymmé
trie qui crée le phénomèn
e"(P. Curie,
1894)
1960:M E
1961:P H
Cr2O3
1960: Theoretically not well understood Small effect (10-5) Limited choice of compounds
2000: New theoretical concepts "Giant" effects: induction of phase transitions New materials: "magnetoelectricity on design"
Review:J. Phys. D 38, R123 (2005)
D.N. Astrov, JETP 11, 708 (1960)
V.J. Folen, PRL 6, 607 (1961)
1985 1990 1995 2000 20050
20
40
60
80
100
120
140
160
Pub
licat
ions
/ ye
ar
Year1985 1990 1995 2000 2005
0
20
40
60
80
100
120
140
160
Pub
licat
ions
/ ye
ar
Year
Generating Large Magnetoelectric Effects
Limitation of the magnetoelectric effect:
Cannot be larger than the geometric mean of electric and magnetic permeability [W. F. Brown, R. M. Hornreich, S. Shtrikman, Phys. Rev. 168, 574 (1968)]
ij2 < ii
e jjm
Yes!! They are called multiferroics!
Do ferroelectric ferromagnetics exist?
Largest: in ferroelectric ferromagnetics
Large magnetoelectric effects:
In ferroelectric samples In ferromagnetic samples
What is a “Multiferroic”?
“Crystals can be defined as multiferroic when two or more of the xprimary ferroic properties are united in the same phase.”
Hans Schmid (University of Geneva, Switzerland) in: M. Fiebig et al. (ed.), Magnetoelectric Interaction Phenomena in Crystals, (Kluwer, Dordrecht, 2004)
Primary ferroic formation of switchable domains:
Ferromagnetism Ferroelectricity Ferroelasticity Ferrotoroidicity
spontaneous spontaneous spontaneous spontaneousmagnetization polarization strain magnetic vortex
Extension to anti-ferroic forms of ordering:
Compounds consisting of multiferroic sublattices (one or more of) whose primary ferroic properties cancel in the macroscopic crystal
Excludes anti-ferroic forms of ordering
N S
What is a Composite Multiferroic?
Constituent 1:PiezoelectricBaTiO3
PbZr1-xTixO3 (PZT)Ba0.8Pb0.2TiO3
Bi4Ti3O12
PVDFPbMg1/3V2/3O3 ...
Constituent 2:MagnetostrictiveCoFe2O4
Tb1-xDyxFe2 (= Terfenol-D)LiFe5O8
YIGPermendur ...
Magnetic field magnetostrictive deformation Transfer of deformation constituent 2 constituent 1 Deformation via piezoelectric effect voltage
CompositePseudo-magnetoelectric End compounds are not
magnetoelectric!
Magnetoelectric effect is a product effect!
1: piezoelectric
2: magnetostrictive
1
2
layered particulate
First Composite Magnetoelectric Effect
BaTiO3/CoFe2O4
Result:
Value of the magnetoelectric pseudo effect in BaTiO3/CoFe2O4:
dE/dH = 130 mV/cmOe
= 720 pT/Vm-1
Compare to best single-phase magnetoelectrics:
Cr2O3: = 4.13 pT/Vm-1
TbPO4: = 36.7 pT/Vm-1
No significant advances on this initial result until the year 2000!
Measuring Magnetoelectric Response in Composites
0 Time
H0
~1
0 kO
e
00 Time
H()
~1
0 O
e
0
= 100 Hz – 1 MHz
0 Time
V()
0
V =101...5 mV/cmOe
Vmax,
Hmax,
The composite ME effect is an AC effect
Linear response for
small intervals only
Hmax,
G. Srinivasan et al.,Phys. Rev. B 67, 014418 (2003)
Self-Assembled Nanocomposite Multiferroics
ME coupling and phase control also observed !
Ferromagnetic
CoFe2O4 pillars
Ferroelectric BaTiO3
matrix
SrTiO3 substrate
Ferroelectric properties
Ferromagnetic properties
H. Zheng et al., Science 303, 661 (2004)
Magnetoelectric Phase Control in Nanocomposites
Force microscopy on BiFeO3/CoFe2O4
Magnetic20 kOe
Magnetic20 kOe
Electric8 V
1 m
Magnetic control by electric field
MFM before MFM after application of 12 V
Line scans of marked regionsME coupling mediated by strainEstimated: (10 V/cmOe)-1
F. Zavaliche et al., Nano Lett. 5, 1793 (2005)
Natural Single-Phase Multiferroics
Three natural crystals
CongoliteFe3B7O13Cl
ChambersiteMn3B7O13Cl
HubneriteMnWO4
See Cologne work
Ni3B7O13I – A Milestone of Multiferroics Research
Rotation of magnetization by 90° [110] [110] Triggers reversal of ferroelectric polarization [001] [001] First example of magnetoelectric cross-control
E. Ascher, H. Schmid et al., J. Appl. Phys. 37, 1404 (1966)
Ferroelectric Ferromagnets
N S
Likes 3dn with n=0 Likes 3dn with n0N.A. Hill, J. Phys. Chem. B 104, 6694 (2000)
Most promising for applications, but not many compounds exist because...
The existing ferroelectric ferroelectrics are usually anti-ferroic with only a weak ferromagnetic or ferroelectric component:
Tb
Mn
2 O5
Mn3B7O13I
O. Crottaz, Ferroelectrics 204, 45 (1997)
N. Hur, Nature 429, 392 (2004)
The quest for strong ferroelectric ferromagnets at 300 K is still far from being solved!
Magnetic Control of Ferroelectricity in TbMnO3
P
M
TbMnO3
P
M
TbMnO3
Magnetic field triggers a ferroelectric phase transition with polarization rotation by 90° T. Kimura et al., Nature 426, 55 (2003)
See Cologne work
Mag
net
ical
ly d
rive
n
ferr
oel
ectr
icit
y
Magnetic Phase Control by Electric Field in HoMnO3
P63cm
E = 0 E 0
P63cmy
x
y
c z
Ho3
Mn3
O2
a b
2a
4b
~63 ~63~63~63
ab
P63cm
E = 0 E 0
P63cmy
x
y
c z
Ho3
Mn3
O2
Ho3
Mn3
O2
a b
2a
4b
~63 ~63~63~63
ab
T. Lottermoser et al., Nature 430, 541 (2004)
Theory of Multiferroics in Magnetic Spirals
• (P,E) and (M,H) linear coupling when they vary both in space and time: ∂E/∂r ≈ ∂H/∂t
• Seek non-linear coupling, e.g., inhomogeneous magnetic order: third order coupling PM∂M, then magnetically induced electric polarization
• So must search for spiral magnetic order, e.g., TbMnO3 et al.
• Spiral states are characterized by two vectors: Q propagation vector
and e3 = e1 x e2 , spin rotation axis. Therefore for non-collinear magnets:
P ║ e3 x Q
Magnetic Tunability of Multiferroics
How to measure P and ε ? HW problems
Symmetry Breakings Required for Multiferroics
Magnetic order breaks time
reversal symmetry (TRS)
Displacements of O2- breaks inversion symmetry (ISB)
Magnetic exchange interaction (with order - TRSB) causes displacement of Mn3+ - ISB
Cologne Work on Multiferroics – Pyroxenes (AMSi2O6)
Pyroxenes :NaFeSi2O6, LiFeSi2O6 and LiCrFe2Si6
natural mineral (crystal aegirine)
Magnetic properties of NaFeSi2O6
Dielectric properties of NaFeSi2O6
How can you measure the electrical polarization ?
Anisotropy of Polarization Pb and Pc
Phase diagram of NaFeSi2O6
Magnetoelectrics and Multiferroics – The End
• Questions
• Comments
• Suggestions ?
• Future Ideas ?
Pyrocurrent measurements of MnWO7
Cologne Work – TbMnO3
Thermal Expansion and Magnetostriction
Thermal Conductivity and Thermal Expansion
GdMnO3 – Thermal Expansion and Magnetostriction
Ferroelectrics Multiferroics