Ferroelectrics to Magnetoelectrics&Multiferroics Ferroelectrics (Valasek,1920’s): Spontaneous electric polarization (P), e.g., BaTiO 3 (displacive) &

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

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licat

ions

/ ye

ar

Year1985 1990 1995 2000 2005

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20

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60

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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