Man

gan

ite

Man

gan

ite

-- ty

pe

mu

ltif

err

oic

sty

pe

mu

ltif

err

oic

s

J.

Fo

ntc

ub

ert

a

Insti

tut

de C

ièn

cia

de M

ate

rials

de B

arc

elo

na,

CS

IC

Bellate

rra, C

ata

lun

ya, S

pain

22

Obje

ctiv

es

Obje

ctiv

es

Ove

rvie

w the m

ain

str

uct

ura

l chara

cterist

ics

of th

e s

imple

st A

MnO

3oxi

des

Ove

rvie

w their m

agnetic

and d

iele

ctric

chara

cterist

ics

and it

s co

nnect

ion to

stru

ctura

l arr

angem

ents

; in

part

icula

r th

e

occ

urr

ence

and e

ventu

al c

oexi

stence

of

bife

rroic

ord

ering

Ove

rvie

w s

om

e e

xperim

enta

l evi

dence

s of

magneto

ele

ctric

couplin

g

33

Index

Index

Str

uct

ura

l tre

nds

Requirem

ents

for

occ

urr

ence

of m

agnetis

m

and ferr

oele

ctrici

ty.

Coexi

stence

of m

agnetis

m a

nd

ferr

oele

ctrici

ty: M

ate

rial’s

resp

onse

:M

ag

ne

tism

with

ou

t 3

dn

(no

n-3

d m

ag

ne

tism

) F

err

oe

lect

rici

ty w

itho

ut

off

-ce

nte

rin

g

The A

MnO

3zo

o:

BiM

nO

3ca

se; F

M &

FE

AM

nO

3: hexa

gonal f

am

ily; A

F &

FE

AM

nO

3: o

rth

orh

om

bic

fa

mily

; A

F b

ut N

ot F

EA

nd

in b

etw

ee

n ?

44

Str

uct

ura

l tre

nds

Str

uct

ura

l tre

nds

Idea

l P

erovsk

ite

stru

cture

O

Mn

La

55

Str

uct

ura

l tre

nd

s :

AM

nO

Str

uct

ura

l tre

nd

s :

AM

nO

33

He

xa

go

na

l

O1

O2

O3

O4

Ort

ho

rho

mb

ic

66

Str

uct

ura

l tre

nd

s :

AM

nO

Str

uct

ura

l tre

nd

s :

AM

nO

33

He

xa

go

na

lO

rth

orh

om

bic

77

Str

uct

ura

l tre

nds

Str

uct

ura

l tre

nds

Pb

nm

a=

5.2

6Å

b=

5.8

5Å

c=7.3

6Å

Pb

3cm

a=

6.1

4Å

c=11.4

0Å

88

Ele

ctro

nic

str

uct

ure

of

oE

lect

ronic

str

uct

ure

of

o--

and h

and h

-- AM

nO

3A

Mn

O3

Ort

horh

om

bic

manganites

Hexagonal m

anganites

Jah

n-T

elle

r act

ive

e g t 2g

3z2

-r2

x2-y

2

xz

,yz

xy

e g t 2g

x2-y

2

yz

xz

xy3z2

-r2

Jah

n-T

elle

r in

act

ive

99

Ele

ctro

nic

effect

s on s

truct

ure

: E

lect

ronic

effect

s on s

truct

ure

: co

opera

tive J

T d

isto

rtio

n a

nd o

rbita

l ord

ering

coopera

tive J

T d

isto

rtio

n a

nd o

rbita

l ord

ering

10

10

Ele

ctro

nic

effect

s on s

truct

ure

:E

lect

ronic

effect

s on s

truct

ure

:co

opera

tive J

T d

isto

rtio

n a

nd o

rbita

l ord

ering

coopera

tive J

T d

isto

rtio

n a

nd o

rbita

l ord

ering

Nd

Mn

O3

11

11

Str

uct

ure

: B

iMn

OS

tru

ctu

re :

BiM

nO

33

Dis

tort

ed

Ort

ho

rho

mb

ic p

ero

vsk

ite

: m

on

ocli

nic

12

12

Str

uct

ure

: B

iFe

OS

tru

ctu

re :

BiF

eO

33

C. Edere

rand N

. Spald

ing

13

13

Re

qu

ire

me

nts

fo

r o

ccu

rre

nce

of

ma

gn

etis

m

Re

qu

ire

me

nts

fo

r o

ccu

rre

nce

of

ma

gn

etis

m

An a

tom

istic

vie

w:

Ma

gn

etis

m:

pa

rtia

lly f

ille

d 3

dn

sta

tes

Ma

gn

etis

mIn

sula

tin

gLoca

lized a

tom

ic m

om

ents

3d

xru

le

3d

8:

Ni2

+:

NiO

(AF)

3d

7:

Co

2+

: C

oO

(AF)

3d

6:

Fe

2+

: Fe

O(A

F)

3d

5:

Fe

3+

:Fe

2O

3(A

F);

B

iFe

O3

(AF)

3d

4:

Mn

3+

:M

n2O

3(A

F);

La

Mn

O3

(AF)

BiM

nO

3(F

M !

!)

14

14

Orb

ital o

rde

rin

g a

nd

su

pe

rexc

ha

ng

e in

tera

ctio

ns

Orb

ital o

rde

rin

g a

nd

su

pe

rexc

ha

ng

e in

tera

ctio

ns

•S

up

erex

cha

ng

e m

ag

net

ic i

nte

ract

ion

s: i.

eM

n3

+-O

-Mn

3+

: 3d

4-2

p6-3

d4

•G

oo

den

ou

gh

-Ka

na

mo

riru

les

15

15

Requirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

tyR

equirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

ty

Insu

lato

rs

Most

wid

ely u

sed

fer

roel

ectr

ics

are

p

ero

vsk

ites

(A

BO

3)

At

T<

TC

ther

e is

a s

tru

ctu

ral

dis

tort

ion

to

a l

ow

er s

ym

met

ry

Th

e p

rese

nce

of

elec

tric

dip

ole

s im

pli

es t

ha

t th

e u

nit

cel

l ca

n n

ot

be

cen

tro

sym

met

ric.

Lo

wer

ing

en

erg

y a

nd

sy

mm

etry

by

ato

mic

dis

pla

cem

ents

Ato

mic

dis

pla

cem

ent

of

TM

is

favore

d i

n 3

d0

con

fig

ura

tio

ns

(d0-

rule

)i.

e. B

aT

iO3

16

16

Requirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

tyR

equirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

ty

Typic

al exam

ple

s.BaTiO

3:

Ba-O

io

nic

bond;

Ti4

+:

3d

0-O

2p

6co

vale

ncy

rele

vant

Ste

reoch

em

icalact

ivity o

f lo

ne-p

airs

of

the larg

e A

-ions

in

ABO

3cr

eating d

ipole

s as

in P

bTiO

3.

Pb

6s

and O

2p h

ybridiz

ation r

ele

vant

and t

unes

the T

i-O

hybridiz

ation

Pb

2+Ti4

+O

3:

Pb

2+:

[Xe]4

f145d

106s2

6p

0

Notice

that

they

can b

e d

esc

ribed a

s “n

p0

“(a

s above

) th

us

form

ing

ns1

np

1exc

ited st

ate

s by

mix

ing w

ith

ns2

(only

perm

itte

d if non

centr

o-s

ymm

etr

ic)

Drivi

ng f

orc

e f

or

off

-cente

ring. Ja

hn

Telle

r 2nd o

rder

ininam

onia

am

onia

NH

NH

33inin

am

onia

am

onia

NH

NH

33

17

17

Requirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

tyR

equirem

ents

for

occ

urr

ence

of fe

rroele

ctrici

ty

Lo

ne

pa

irs a

nd

A

-B c

ha

rge

tra

nfe

r

18

18

Requirem

ents

for

occ

urr

ence

of fe

rrom

agnetis

m

Requirem

ents

for

occ

urr

ence

of fe

rrom

agnetis

m

and F

err

oele

ctrici

tyand F

err

oele

ctrici

tyCoexis

tence

of

Magnetism

and F

err

oele

ctrici

ty r

equires

that

off

-cente

ring ions

diffe

r fr

om

those

carr

yin

g (

3d)

magnetic

mom

ent.

Contr

ary

to B

aTiO

3

Four

route

s:

1.

Ste

reoch

em

icalact

ivity o

f lo

ne-p

airs

of

the larg

e A

-ions

in A

BO

3cr

eating d

ipole

s, w

hile

mom

ent

resi

des

at

B

site

s as

in B

iMnO

3or

BiF

eO

3

2.

Geom

etr

ically

driven

ferr

oele

ctric,

such

as

h-Y

MnO

3

3.

Non-c

entr

osy

mm

etr

icst

ruct

ure

s re

sultin

g f

rom

fr

ust

rate

d m

agnetic

ord

ering:

A.

Com

peting inte

ract

ions

( J

>0, J’

<0)

, su

ch a

s o-T

bM

nO

3

B.

Geom

etr

ical fr

ust

ration, su

ch a

s in

RM

n2O

5

4.

Non-c

entr

osy

mm

etr

icst

ruct

ure

s re

sultin

g f

rom

charg

eord

ering

19

19

1.

1.

Bife

rroic

s and lo

ne

Bife

rroic

s and lo

ne

-- pairs

pairs

Ste

reoch

em

icalact

ivity o

f lo

ne-p

airs

of

the larg

e A

-ions

in

ABO

3cr

eating d

ipole

s, w

hile

mom

ent

resi

des

at

B s

ites

as

in

BiF

eO

3or

BiM

nO

3

Exam

ple

s.

Bi3

+M

n3+O

3: Bi: [

Xe]4

f145d

106s2

6p

3

20

20

1.

1.

Lone

Lone

-- pair b

iferr

oic

(F

E &

FM

) B

iMnO

pair b

iferr

oic

(F

E &

FM

) B

iMnO

33

N. Spald

ing

21

21

1.

1.

Lone

Lone

-- pair b

iferr

oic

(A

F &

FE

) B

iFeO

pair b

iferr

oic

(A

F &

FE

) B

iFeO

33

BiF

eO

BiF

eO

33R

ho

mb

oh

ed

ral

sym

me

try (

R3

c)

Ram

esh

et

al Sci

ence

22

22

1.

1.

Lone

Lone

-- pair b

iferr

oic

(A

F &

FE

) B

iFeO

pair b

iferr

oic

(A

F &

FE

) B

iFeO

33

BiF

eO

BiF

eO

33

http://a

rxiv

.org

/ftp

/arx

iv/p

apers

/0706/0

706.0

404.p

df

@RT

23

23

2. G

eom

etr

ically

drive

n ferr

oele

ctric:

h2. G

eom

etr

ically

drive

n ferr

oele

ctric:

h-- A

MnO

AM

nO

33

Origin

of

Ferr

oele

ctrici

ty in Y

MnO

3lik

e h

exagonal st

ruct

ure

s ?

Notice

that:

Mn

3+:

is

a n

on-d

0sy

stem

(3d

4)

Y3+

:th

ere

are

no lone-p

airs

(nsx

xnp

x)

Calc

ula

tions

show

no s

ignific

ant

hybridiz

ation b

etw

een Y

-4d a

nd O

2p.

Charg

es

close

to ionic

valu

e. N

o

hybridiz

ation.

The s

mall

size

of

the Y

dete

rmin

e

the d

iffe

rent

stru

cture

of

LaM

nO

3and Y

MnO

3.

At

TN, th

ere

is

a b

uck

ing o

f th

e

MnO

5 b

ipyra

mid

s. M

nre

main

s at

its

cente

r.N

O O

FF-C

EN

TERIN

G

Dis

pla

cem

ent

of

Y ions

alo

ng

hexagonal axis

rela

tive t

o M

nO

5:

Cre

ate

s an e

lect

ric

dip

ole

.

24

24

2. G

eom

etr

ically

drive

n ferr

oele

ctric:

h2. G

eom

etr

ically

drive

n ferr

oele

ctric:

h-- A

MnO

AM

nO

33

25

25

3. A

F

err

oele

ctrici

ty in

fru

stra

ted m

agnets

: 3. A

F

err

oele

ctrici

ty in

fru

stra

ted m

agnets

: M

agnetic

drive

n o

ffM

agnetic

drive

n o

ff-- c

ente

ring,

cente

ring,

i.ei.eoo

-- TbM

nO

TbM

nO

33 26

26

3. A

F

err

oele

ctrici

ty in

fru

stra

ted m

agnets

: 3. A

F

err

oele

ctrici

ty in

fru

stra

ted m

agnets

: m

agnetic

drive

n o

ffm

agnetic

drive

n o

ff-- c

ente

ring,

cente

ring,

i.ei.eoo

-- DyM

nO

DyM

nO

33

DyM

nO

3 Ma

gn

eti

c f

ield

tu

na

bil

ity

of

ma

gn

eti

c f

err

oe

lectr

ics

27

27

3. A

3. A

Ma

gn

etic

dri

ven

off

Ma

gn

etic

dri

ven

off

-- ce

nte

rin

g o

cen

terin

g o

-- (E

u(E

u0

.75

0.7

5YY

0.2

50

.25)M

nO

)Mn

O33

An

alo

go

us t

o T

bM

nO

3b

ut

wit

ho

ut

ma

gn

eti

c

mo

me

nts

at

A-s

ite

s.

A

sim

ple

r ca

se

.

(Ch

eo

ng

et

al.

Na

ture

M

at.

6,

13

20

07

)

•In

co

mm

en

su

rate

sin

uso

ida

l o

rde

r a

t

40

-45

K

•C

om

me

nsu

rate

A

F

ord

eri

ng

at

38

-41

K•

Re

-en

tra

nce

to

in

co

mm

en

su

rate

sin

uso

ida

l o

rde

rin

g a

t 2

0-

25

K•

Ord

eri

ng

of

RE

(e

ve

ntu

all

y)

at

T <

10

K

28

28

3. B

3. B

Non

Non

-- co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

fr

ust

ratio

n: R

eM

nfr

ust

ratio

n: R

eM

n22OO

55

29

29

3. B

3. B

Non

Non

-- co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

fr

ust

ratio

n: R

eM

nfr

ust

ratio

n: R

eM

n22OO

55

GE

OM

ET

RIC

ALLY

IN

DU

CE

D M

AG

NE

TIC

FR

US

TR

AT

ION

30

30

3. B

3. B

Non

Non

-- co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

fr

ust

ratio

nfr

ust

ratio

n

31

31

3. B

3. B

Non

Non

-- co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

co

llin

ea

r m

ag

ne

tic o

rde

rin

g b

y g

eo

me

tric

fr

ust

ratio

nfr

ust

ratio

n

Tb

Mn

2O

5

32

32

Cla

ssifi

catio

n o

f fe

rroele

ctrics

Cla

ssifi

catio

n o

f fe

rroele

ctrics

33

33

Couplin

gP

and

M(C

he

on

g a

nd

Mo

sto

vo

y.

Na

ture

Ma

t. 6

, 1

3 2

00

7)

1.

Non-lin

ear

P a

nd M

couplin

g a

lways

exis

t in

solid

s.

It a

rise

s fr

om

inte

rpla

y o

r ch

arg

e, sp

ins,

orb

its

and latt

ice.

It is

genera

lly s

mall

E ~

P2

M2

This

quadra

tic

term

acc

ounts

for

the s

mall

change o

f die

lect

ric

const

ant

obse

rved a

t th

e m

agnetic

transi

tion in h

-AM

nO

3and B

iMnO

3

2.

If t

he m

agnetiza

tion is

not

hom

ogeneous

a t

hird o

rder

contr

ibution

may e

xis

t: E

~ P

MM

.For

a c

ubic

cry

stal

HERE I

T I

S W

ERE F

RU

STRATIO

N A

ND

CO

MPLEX S

PIN

ARRAN

GEM

EN

TS

PLAY A

RO

LE.

3. H

ow

magnetic

sp

irals

induce

ferr

oele

ctrici

ty3. H

ow

magnetic

sp

irals

induce

ferr

oele

ctrici

ty

34

34

SP

IRA

L O

RD

ER

ING

Dzya

losh

insk

ii-M

ori

ya

HD

M~

Dn

, n

+1

Sn

xS

n+

1

D ~

x x

rn

, n

+1

Ferr

oele

ctrici

ty a

rise

s fr

om

exch

age

strict

ion:

latt

ice r

ela

xation in a

magnetic

ord

ere

d s

tate

.D

zya

losh

insk

ii-M

ori

ya

in

du

ce

s o

n-p

ha

se

sh

ift

of

bri

dg

ing

lig

an

ds

(O-2

) a

nd

th

us a

po

lar

sta

te:

P// e

3x

Q

3. H

ow

magnetic

sp

irals

induce

ferr

oele

ctrici

ty3. H

ow

magnetic

sp

irals

induce

ferr

oele

ctrici

ty

35

35

4. E

lect

ronic

(C

harg

e o

rdere

d)

Ferr

oele

ctric

4. E

lect

ronic

(C

harg

e o

rdere

d)

Ferr

oele

ctric

An

ex

am

ple

: Lu

Fe

2O

4

Fro

m C

heong e

t al N

atu

re M

at.

6, 13 (

2007)

36

36

4. E

lect

ronic

(C

harg

e o

rdere

d)

Ferr

oele

ctric

4. E

lect

ronic

(C

harg

e o

rdere

d)

Ferr

oele

ctric

LuFe

2O

4

Quest

ionable

?

37

37

Magnetis

m a

nd m

agnetic

pro

pert

ies

Magnetis

m a

nd m

agnetic

pro

pert

ies

1.

Ferr

om

agnetism

via

Mn

3+:

3d

4-O

rbital ord

ering in

BiM

nO

3:

Uniq

ue !

2.

Antife

rrom

agnetism

of

BiF

eO

3

3.

Antife

rrom

agnetism

in h

exagonal -A

MnO

3

4.

Antife

rrom

agnetism

in o

rthorh

om

bic

-AM

nO

3

38

38

1. F

err

om

agnetis

m a

nd o

rbita

l ord

ering: B

iMnO

1. F

err

om

agnetis

m a

nd o

rbita

l ord

ering: B

iMnO

33

Mo

reir

ad

os S

an

tos 2

00

2

39

39

1.

1.

Magneto

ele

ctric

couplin

g in

BiM

nO

Magneto

ele

ctric

couplin

g in

BiM

nO

33

40

40

2. A

ntif

err

om

agnetis

m in

BiF

eO

2. A

ntif

err

om

agnetis

m in

BiF

eO

33

41

41

3. H

exag

on

al M

an

gan

ites:

su

mm

ary

of

pro

pert

ies

an

tife

rro

mag

neti

co

rde

rin

gte

mp

era

ture

(K

)

ferr

oele

ctr

ico

rde

rin

gte

mp

era

ture

(K

)a (

Å)

c (

Å)

ScM

nO

3129

~ 9

00

5.8

33

11.1

7

Yb

Mn

O3

87

983

6.0

62

11.3

6

914

Ho

Mn

O3

76

~ 9

00

6.1

42

11.4

2

ErM

nO

380

830

6.1

12

11.4

0

Tm

Mn

O3

86

~ 9

00

6.0

92

11.3

7

YM

nO

380

~ 9

00

11.3

96.1

39

6.0

42

Lu

Mn

O3

96

11.3

7 42

42

3. A

ntif

err

om

agnetis

m in

h3. A

ntif

err

om

agnetis

m in

h-- A

MnO

AM

nO

33: 2D

: 2D

tr

iangula

r la

ttic

etr

iangula

r la

ttic

eO

1

O2

O3

O4

Mn

In-p

lane in

tera

ctio

ns

Supere

xchange:

Inte

rpla

ne

inte

ract

ions

Super-

super-

exc

hange:

~ 1

30º

~ 1

20º

43

43

3. H

exa

gonal A

MnO

3. H

exa

gonal A

MnO

33:: F

rust

rate

d

antif

err

om

agnets

Tri

angula

r la

ttic

e w

ith c

om

pet

ing A

F i

nte

ract

ions

-600

-400

-200

0200

400

600

800

1000

0

100

200

300

400

500

CW

= -

500 K

CW

/TN =

6.7

1/(mol-Oe/emu)

Tem

per

ature

(K

)

44

44

3.

3. A

ntif

err

om

agnetis

m in

h-A

MnO

3: D

iffere

nt

spin

config

ura

tions

Fro

m N

eutr

on d

iffr

act

ion d

ata

severa

l sp

in c

onfigura

tion c

an b

e p

ropose

d

repre

senta

tion

repre

senta

tion

repre

senta

tion

repre

senta

tion

A. M

uñ

oz

et a

l., P

RB

(2

00

0)

45

45

3.

Antif

err

om

agnetis

m in

h-A

MnO

3:

spin

ord

ering

A.

Mu

no

z et

al.

, P

RB

(2

00

0)

048

20

60

100

140

048

1

Intensity (103 counts)

3

2 (

deg

.)

13

a (

Å)

= 6

.1208(1

)

b (

Å)

= 1

1.4

015(2

)

V (

Å3)

= 3

69.9

1(1

)

a (

Å)

= 6

.1208(1

)

b (

Å)

= 1

1.4

015(2

)

V (

Å3)

= 3

69.9

1(1

)

Magnetic

Mom

ent (m

B)

3.3

0(2

)

Magnetic

Mom

ent (m

B)

3.2

5(2

)

Relia

bili

ty f

act

ors

Rp

= 5

.79 %

Rw

p=

7.9

3 %

Rm

ag=

7.8

8 %

c2=

2.7

0

Relia

bili

ty f

act

ors

Rp

= 5

.83 %

Rw

p=

7.9

8 %

Rm

ag=

7.3

5 %

c2=

2.7

4

J P

ark

, et

al.

,

Ap

pli

ed P

hys

ics

A (

20

02

)

46

46

3.

Ma

gn

eti

c a

nis

otr

op

y o

f h

-AM

nO

3

T =

5K

Adapte

d f

rom

Fie

big

et

al

47

47

T =

5K

3.

Antif

err

om

agnetis

m in

h-A

MnO

3: sp

in o

rdering –

2nd O

HG

YM

nO

3

Sc

Mn

O3

YM

nO

3

ErM

nO

3

Ad

ap

ted

fro

m M

. F

ieb

ige

t a

l, P

RB

, P

RL

,..

48

48

3. A

ntif

err

om

agnetis

m in

h3. A

ntif

err

om

agnetis

m in

h-- A

MnO

AM

nO

33: m

agnetic

: m

agnetic

anis

otr

opy

anis

otr

opy

We

ak

in

-pla

ne

ma

gn

eti

c a

nis

otr

op

y:

Ma

nif

este

d

as f

ast

the

rma

l su

pp

ressio

n o

f e

xch

an

ge

bia

s a

nd

tra

inin

g e

ffe

cts

1.

Exc

hange b

ias

well

visi

ble

.2.

Vert

ical a

nd h

orizo

nta

l shift

(both

pre

dic

ted b

y so

me m

odels

)3.

Tra

inin

g e

ffect

-200

-150

-100

-50

050

100

150

200

-505

2nd

H, O

e

m x10-5, emu

1st

FC

fro

m 1

00K

at +

300

0 O

e

Subst

rate

ST

O(1

11)

Ele

ctro

de:P

t

AF

and

FE

h-Y

Mn

O3

Fe

rro

ma

gn

et:

Perm

all

oy

Subst

rate

ST

O(1

11)

Ele

ctro

de:P

t

AF

and

FE

h-Y

Mn

O3

Fe

rro

ma

gn

et:

Perm

all

oy

1010

0050100

020406080

HEB (Oe)

HC (Oe)

T (

K)

TN

(bulk

)

X.

Ma

rti

et

al

AP

L 2

00

5

49

49

3. A

ntif

err

om

agnetis

m in

h3. A

ntif

err

om

agnetis

m in

h-- A

MnO

AM

nO

33

•N

otice

the a

bse

nce

of

a w

ell

defined p

eak a

t T

N

•For

H p

erp

endic

ula

r to

pla

ne:

susc

eptibili

ty s

hould

be c

onst

ant

TN)belo

w T

N

•For

H p

ara

llel to

pla

ne a

nd f

or

a t

riangula

r sp

in a

rrangem

ent

TN)

50

50

3. M

agneto

ele

ctric

couplin

g in

h3. M

agneto

ele

ctric

couplin

g in

h-- A

MnO

AM

nO

33

h-Y

Mn

O3

51

51

3. M

agneto

ele

ctric

couplin

g in

h3. M

agneto

ele

ctric

couplin

g in

h-- A

MnO

AM

nO

33

Sp

in-p

ho

no

nco

up

lin

g i

n

h-A

Mn

O3

52

52

3. M

agneto

ele

ctric

couplin

g in

h3. M

agneto

ele

ctric

couplin

g in

h-- H

oM

nO

HoM

nO

33

53

53

3. M

agneto

ele

ctric

couplin

g in

h3. M

agneto

ele

ctric

couplin

g in

h-- H

oM

nO

HoM

nO

33

54

54

3. M

agneto

ele

ctric

couplin

g in

Lu

3. M

agneto

ele

ctric

couplin

g in

Lu

-- AM

nO

AM

nO

33

Sim

ilarl

y r

eport

ed f

or

h-Y

Mn

O3

55

55

3.

3.

Magneto

stru

ctura

lM

agneto

stru

ctura

lco

uplin

g in

hco

uplin

g in

h-- L

uM

nO

LuM

nO

33

bc

4.

4.

Ort

ho

rho

mb

icO

rth

orh

om

bic

AM

nO

AM

nO

33::

mo

du

late

dm

od

ula

ted

an

tife

rro

ma

gn

eti

c

str

uc

ture

sa

nti

ferr

om

ag

ne

tic

s

tru

ctu

res

•AF

ord

ering o

f ato

mic

m

om

ents

in Y

MnO

3

•In

o-Y

Mn

O3, sp

in

com

pensa

tion o

f (0

01)

and (

001)

surf

ace

s occ

urs

only

ove

r a f

ew

la

ttic

e c

onst

ants

.

Brinks

et al,

PR

B 6

3, 094411

3b

a

b

c

3b

a

b

c

3b

a

b

c

Pb

nm

sett

ing

(YM

nO

3):

= 1

44º

a =

5.2

6 Å

b =

5.8

5 Å

c =

7.3

6 Å

57

57

4. A

ntif

err

om

agnetis

m in

o4. A

ntif

err

om

agnetis

m in

o-- A

MnO

AM

nO

33

•O

rthorh

om

bic

Pbnm

(5.3

Å,

5.8

5 Å

and 7

.49 Å

)

•TN

( ~

45 K

) L

ong r

ange

magnetic

ord

er

•At T

35K

magnetic

str

uct

ure

m

odula

ted (

a s

ingle

Fourier

com

ponent, w

ith Q

= (

0, q, 0)

with

q=

0.2

7)

allo

ws

to

desc

ribe the s

truct

ure

)

•At T

15K

de-p

hase

d

sinuso

idal m

odula

tion alo

ng

two o

rthogonal d

irect

ions:

elli

ptic

al s

piral.

58

58

4. M

agneto

ele

ctric

couplin

g in

o4. M

agneto

ele

ctric

couplin

g in

o-- A

MnO

AM

nO

33

Toku

ra’s

gro

up

PR

B 9

2, 257201 (

2004)

59

59

4. M

agneto

ele

ctric

couplin

g in

o4. M

agneto

ele

ctric

couplin

g in

o-- A

MnO

AM

nO

33

60

60

4. M

agneto

ele

ctric

couplin

g in

o4. M

agneto

ele

ctric

couplin

g in

o-- A

MnO

AM

nO

33

Post

er

P3.2

3 T

hurs

day

Sym

po

sium

H

Ort

horh

om

bic

YM

nO

Ort

horh

om

bic

YM

nO

33::

magneto

capaci

tance

magneto

capaci

tance

•Peak o

f d

iele

ctr

ic c

on

sta

nt

clo

se t

o t

he T

N.

•In

co

ntr

ast

to d

ata

rep

ort

ed

fo

r sin

gle

cry

sta

ls,

(T)

peaks a

t T

> T

N

010

2030

4050

20222426

r (film)

Tem

pera

ture

(K

)

0,6

0,8

1,0

1,2

1,4

1,6

f =

10

5 Hz

Vo

sc =

1V

0Hap

pl=

0.0

2T

FC

m (10-5 emu)

ZF

C

X. M

art

i et

al.

J. M

at.

Res.

In p

ress

YM

nO

3si

ngle

cry

stal-

Lore

ntz

et

al. P

RB

62

62

5. M

agneto

ele

ctric

couplin

g in

o5. M

agneto

ele

ctric

couplin

g in

o-- T

bM

nO

TbM

nO

33

T<

TN

(45

K)

Sin

uso

idal m

odula

ted s

pin

st

ruct

ure

with

mom

ents

alo

ng

b-a

xis.

It does

not bre

ak

the

sym

metr

y alo

ng c

-axi

s.

T<

25K

Mom

ents

form

an e

lliptic

al

spiral .

The s

ymm

etr

y alo

ng c

-axi

s is

bro

ken. It a

llow

s fin

ite P

M. K

enze

lmann

et al,

PR

L 0

87206

(20

05

)

Concl

usi

on:F

E a

ppears

at th

e tra

nsi

tion b

etw

een a

in

com

mensu

rate

dlo

ngitu

din

al (

sinuso

idal) s

truct

ure

to

a in

com

mensu

rate

dsp

iral s

truct

ure

that bre

aks

the

spatia

l inve

rsio

n s

ymm

etr

y.

63

63

Oth

er

co

up

lin

g m

ech

an

ism

sO

the

r co

up

lin

g m

ech

an

ism

s

•m

utu

al

cla

mp

ing

of

ma

gn

eti

c a

nd

fe

rro

ele

ctr

ic

do

ma

ins,

as i

n h

-AM

O3

Fie

big

et

al.,

Natu

re 4

19,

818 (

2002)

EXPLO

IT F

OR P

RACTIC

AL A

PPLIC

ATIO

NS

64

64

Ex

plo

itin

g c

ou

ple

d F

E &

AF d

om

ain

s o

f E

xp

loit

ing

co

up

led

FE

& A

F d

om

ain

s o

f

bif

err

oic

ma

teri

als

b

ife

rro

ic m

ate

ria

ls

V.

V.

La

ukh

inL

au

kh

inet al P

RL

et al P

RL

97, 227201 (

2006)

Subst

rate

ST

O(1

11)

Ele

ctro

de:P

t

AF

and F

Eh

-YM

nO

3

Fe

rro

ma

gn

et:

Pe

rma

llo

y

AF

/FE

FM

AF

/FE

FM

V

65

65

Ex

plo

itin

g c

ou

ple

d F

E &

AF d

om

ain

s o

f E

xp

loit

ing

co

up

led

FE

& A

F d

om

ain

s o

f

bif

err

oic

ma

teri

als

b

ife

rro

ic m

ate

ria

ls

Tem

pera

ture

dep

en

den

ce

06

01

20

18

02

40

30

03

60

21

.31

21

.32

21

.33

T=

10

0K

R ()

(d

eg

)

18

.41

18

.42

18

.43

18

.44

T=

5 K

R ()

H =

50

Oe

Ele

ctr

ic-f

ield

su

pre

ssio

no

fH

bia

s

V.

V.

La

ukh

inL

au

kh

inet al P

hil.

et al P

hil.

Ma

gM

ag

. 87, 183 (

2007)

. 87, 183 (

2007)

66

66

Sum

mary

Sum

mary

1.

Ste

reoch

em

icalact

ivity o

f lo

ne-p

airs

•W

e h

ave

revi

sed d

iffe

rent

appro

ach

es,

so f

ar

exp

lore

d,

to induce

biferr

oic

behavi

or

in s

ingle

phase

mate

rials

of

the larg

e A

-ions

in A

BO

3cr

eating d

ipole

s, w

hile

mom

ent

resi

des

at

B

site

s as

in B

iMnO

3or

BiF

eO

3

2.

Geom

etr

ically

driven

ferr

oele

ctrics

, su

ch a

s h-Y

MnO

3

3.

Non-c

entr

osy

mm

etr

icst

ruct

ure

s re

sultin

g f

rom

fr

ust

rate

d m

agnetic

ord

ering:

A.

Com

peting inte

ract

ions

( J

>0, J’

<0)

, a

s in

o-T

bM

nO

3

B.

Geom

etr

ical fr

ust

ration, a

s occ

urr

ing in R

Mn

2O

5

4.

Non-c

entr

osy

mm

etr

icst

ruct

ure

s re

sultin

g f

rom

charg

eord

ering, su

ch a

s LuFe

2O

4