Magnetoelectric Multiferroics - MAGNETISM.eumagnetism.eu/esm/2007-cluj/slides/doerr1-slides.pdfMagnetoelectric Multiferroics Kathrin Dörr, ... Faraday rotation ... good elastic coupling

1

Magnetoelectric Multiferroics

Kathrin Dörr, IFW Dresden, Postfach 270116, 01171 Dresden, Germany

ESM 2007, Cluj-Napoca, 14 September 2007

Thanks to M. Fiebig

History and fundamentals

Single-phase multiferroics

Composite multiferroics

Experimental techniques

Summary, Literature

2

What is a multiferroic ?

“Crystals can be defined as multiferroic when two or more of theprimary ferroic properties [...] are united in the same ph ase.”

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 Ferrot oroidicityspontaneous spontaneous spontaneous spontaneousmagnetization polarization strain magnetic vortex

Excludes anti-ferroicforms of ordering

N S+ − + −+ − + −+ −+ − + −+ −+ −+ −

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

3

Idea of the magnetoelectric effect

3


3


magnetoelectriceffect

magnetic shapememory effect

4

Quantification of the ME effect

Free energy of magnetoelectric materials with „mixed term s“ in E, H:

F(Ei , Hj ) = - α α α α i j Ei Hj - ½ββββijk EiHj Hk - ½ γγγγijk EiEj Hk

magnetization: M(E) = - dF / dH

electric polarization: P(H) = - dF / dE requires breaking of time-reversal and space-inversion symmetries

♦♦♦♦ Linear magnetoelectric effect: Pi = ααααij Hj ; Mj = ααααij Ei

“the“ magnetoelectric effect

♦♦♦♦ Higher order terms for ββββ ≠ 0, γγγγ ≠ 0

5

History

"C'est la dissymmétriequi crée le phénomène"(P. Curie, 1894)1894 P. Curie: discussed correlation of

magnetic and electric properties in low-

symmetry crystals

1926 P. Debye: “magneto-elektrischer

Richteffekt“

1957 L. D. Landau, E. M. Lifshitz: “The

magnetoelectric effect is odd with respect to

time reversal and vanishes in materials

without magnetic structure.“

1959 I. E. Dzyaloshinskii: predicted the

magnetoelectric effect in Cr2O3

1960 D. N. Astrov: first observation in Cr2O3

6

History

M ∝∝∝∝ ααααE P ∝∝∝∝ αααα∗∗∗∗H

Cr2O3

D. N. Astrov, JETP 11, 708 (1960) V. J. Folen, PRL 6 , 607 (1961)

7

The revival

Since about the year 2000:

♦ New materials (“designed“

composites) with much larger

ME effect

♦ New theoretical approaches /

concepts

♦ New experimental techniques

(neutron scattering, non-linear

optics)

1985 1990 1995 2000 2005 20100

20

40

60

80

100

120

140

160

180

200

Pub

licat

ions

/ ye

ar

Year

Publications on

"magnetoelectric"

8

Sources of the magnetoelectric effect Limitation of the magnetoelectric effect: ααααij2 < χχχχiie χχχχjjmχχχχii

e: electric susceptibility χχχχjjm: magnetic susceptibility Large in ferroelectric and ferromagnetic samples → multiferroics

W. F. Brown et al., Phys. Rev. 168, 574 (1968)

+ − + −+ − + −+ −+ − + −+ −+ −+ −

“Likes“ 3dn with n=0

N S

“Likes“ 3dn with n≠≠≠≠0

N.A. Hill, J. Phys. Chem. B 104, 6694 (2000)

There are very few magnetic ferroelectrics. (N. Hill alias Nicola Spaldin)






Summary, Literature

9

Single-phase multiferroics: overview

Most are ant i-ferroic in one of

the orders (magnetic / electric)

→→→→ small magnitude of M or P

Multiferroics “unusual“

because they circumvent thed0 / dn problem [1]

[1] C. Ederer and N. A. Spaldin, Curr. Opin. Sol. S tat. Mat. Sci. 9, 128 (05)

• Perovskite type:ABO 3, A2B`B``O 6 (e. g., BiFeO 3, TbMnO 3)

• Hexagonal structure:RMnO3 with R = Sc, Y, Ho-Lu

• Boracites:M3B7O13X with M = Cr, Mn, Fe ...; X = Cl, Br, I

• Orthorhombic BaMF 4 compoundsM = Mg, Mn, Fe, Co, Ni, Zn

and further ones (about 100)

• Non-multiferroic magnetoelectrics:

GdFeO3, LuFe 2O4

Very rare: RT multiferroics

(BiFeO3: ferroelectric + antif.mag)

10

Magnetic control of ferroelectricity: TbMnO 3

ferroelectric

P changes direction in large magnetic fieldT. Kimura et al., Nature 426, 55 (2003)

11

Spin spirals as source of polarization

In TbMnO3, a spiral spin structure and ferroelectricity appear at T ≤ Tlock. Spin spirals break time and space inversion symmetry

(promising for ME effect)

Polarization P ∝∝∝∝ eij x (S i x S j ) proposed (H. Katsura)

H. Katsura et al., PRL 95, 057205 (2005)

Si, Sj: magnetic moments

eij : unit vector connectingsites i, j

P: polarization

js: “spin current“

eij

Si Sj

11a

Spin spirals as source of polarization

A spin spiral can be characte-

rized by the propagationvector k, the rotation plane (jS)

and the cone angle β.

Note: not all spirals cause polarization !

Neutron diffraction: determinespin spiral structure

H. Katsura et al., PRL 95, 057205 (2005)

kP

12

Charge-ordered compounds

D. V. Efremov et al., Nature Mat. 3, 853 (04)

(a) Mn4+ order or

(b) electron hole

at the O ? Intermediate

case (c) with

broken space

inversion

symmetry

a) “site-centered“

b) “bond-centered“

c) intermediate

Transition metal oxides (e. g. Pr1-xCaxMnO3):

eg electrons order in insulating phases

13

HoMnO3

hexagonal structure

ferroelectric at ~870 K

Mn( ): antiferromagnetic, TN = 76 K, TSR = 34 – 40 K

Ho ( ): antiferromagnetic,

order sets in at TSR,

full order at THo = 6 K

P63cm

E = 0

a

2a

4b

P63cm

E = 0

a

2a

4b

Ho3+

Mn3+

O2-

T < TN: P63cm

T < TSR: P63cm

T. Lottermoser, M. Fiebig et al., Nature 430, 541 (2 004)

14

HoMnO3: magnetic phase control by electric field

E

P63cmb

E

P63cmb

E ~ 100 kV cm -1

T. Lottermoser, M. Fiebig et al., Nature 430, 541 (2004)

Mn and Ho magnetic structures are coupled. In electric field, Mn reorients and Ho becomes ferromagnetic.

0 20 40 60 80 100

0

1

2

3

-2 -1 0 1 2-1.0

-0.5

0.0

0.5

1.00

0 10 20 30 40 50 60 70 80

T Ho

TR

TN

a

× 1.5 I

SH(y)

ISH

(x)

ISH

(y)

ISH

(x)

Temperature (K)

SH

inte

nsity

IS

H

E = 0

E ≠ 0

E ≠ 0

c

µ0H

z = 0.5 T

∆Φ =

[Φ(+

E) −

Φ(−

E)]

/2 (

°)

Temperature (K)

E = 0

b

T = 1.4 K

Far

aday

rot

atio

n Φ

(°/

µm)

Magnetic field µ0H

z (T)

Mn

Ho

15

BiFeO3

Switching of FE domains (PFM

tip) ⇒ switching of AFM domains

in BiFeO3 films at 300 K

T. Zhao et al., Nature Mat. 5 (06)

Magnetic(PEEM)

Electric (PFM)

• perovskite type structure

• multiferroic with the highest

ordering temperatures :

ferroelectric: TC = 1103 K

antiferromagnetic: TN = 643 K

(spin spiral)

Application: control the exchange bias by electric field

16

“Electromagnons“

In magnetoelectrics, new excitations /

quasiparticles are possible:

Magnons (spin waves) associated with

dielectric polarization excited by GHz

electric field⇒ “electromagnons“

A. Pimenov et al., Nature Physics 2, 97 (06)

ε1

ν (cm-1)0 30Resonances in the dielectric

function, suppressed by

magnetic field

16

“Electromagnons“

In magnetoelectrics, new excitations /

quasiparticles are possible:

Magnons (spin waves) associated with

dielectric polarization excited by GHz

electric field⇒ “electromagnons“

A. Pimenov et al., Nature Physics 2, 97 (06)

ε2

Resonances in the dielectric

function, suppressed by

magnetic field






Summary, Literature

17

Composite multiferroics create large response M(E) or P(H) at ambient temperatures

ferromagnet: H →→→→ M

ferroelectric: E →→→→ P

+Couple them and

expect:

H →→→→ P, E →→→→ M

multiferroic

composites

Magnets

Tb1-xDyxFe2

La0.7Sr0.3MnO3

CoFe2O4

YIG (garnets)

Fe, Py, ..

Ferroelectrics

BaTiO 3

Pb(Zr,Ti)O 3

SrBi 2Ta2O9

PMN-PT

PVDF, …

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Magnetoelectric coupling

piezoelectricmagnetostrictive

σσσσ1. Mechanical strain

magnet

FEE + + +

E

P- - -

2. Interface charge / bonding effects

a) Field effect

b) Bond effect: change in bonding upon P reversal alter s interfacemagnetization C. G. Duan, E. Y. Tsymbal, PRL 95 (06)

S. X. Dong, D. Viehland et al., APL 85 (04)

H E

20

Types of strain-coupled composites

• Mixed, sintered powders

• Free-standing laminar composites

• Layered thin film structures

• Nanostructured composite films

21

Free-standing laminar composites

J. Ryu et al., Jap. J. Appl. Phys. 40, 4948 (2001)

Piezoelectric and magnetostrictive

components glued or hot-pressedtogether

Example: PZT/Terfenol-D trilayer

magnetoelectric voltage coefficient:

dE/dH = 4.7 V / (cm Oe)

21

Free-standing laminar composites

Piezoelectric and magnetostrictive

components glued or hot-pressedtogether

Huge values at resonances in theAC magnetic field

Sensitive (low noise) magnetic fieldsensors (D. Viehland et al.)

J. Zhai, D. Viehland et al., APL 89, 83507 (06)

22

Layered thin film structures

Heteroepitaxial growth of multilayers on monocrystalline substrates⇒ good elastic coupling at the FE/FM interface⇒ field effect at interfaces⇒ further mechanisms: multiferroic tunnelbarriers depending on electric and magneticfield (see below)

Disadvantage:

Clamping to the substrate , weak strain

Substrate

23

Layered thin film structures

-10 -5 0 5 10

75

80

85

90

95

mag

netiz

atio

n (e

mu

/ cm

3 )

electric field (kV / cm)

La0.7Sr0.3MnO3 (30 nm) / PMN-PT

T = 330 K

µµµµ0H = 10 mT

δεδεδεδεxx = - 0.1 %

-10 -5 0 5 10

-5

0

5

αα αα (

10-8 s

/ m

)


magnetoelectric coupling factor

αααα = µµµµ0 dM / dE ≤ 5⋅⋅⋅⋅10-8 s / m

-10 -5 0 5 10

-0.10

-0.05

0.00

0.05

in-p

lane

str

ain

(%)


T = 300 Kcompressionexpansionpiezo - crystal

magnetic film

Vpiezo

Films on piezoelectric substrate

PMN-PT(001)

C. Thiele, K. D., Phys. Rev. B 75, 054408 (07)

24

Nanocolumnar composites

H. Zheng et al., Science 303, 661 (04)

Two-dimensional structures

(like columns) may show larger

strain on a rigid substrate.⇒ self-organized growth⇒ nanofabrication (templates)

CoFe2O4 - BaTiO3 nanocolumnar film

BTO

CFO

25

Nanocolumnar composites

MFM images,

quadratic area

electrically

written @ -16 V

F. Zavaliche, R. Ramesh et al., Nano Lett. 7, 1586 (0 7)

Local magnetizationelectrically written

26

Field effect experiments

T. Kanki et al., APL 83, 4860 (03) X. Hong et al., PRB 68, 134415 ( 03)

PZT – La0.8Sr0.2MnO3 (4 nm)PZT - La0.9Ba0.1MnO3 (6 nm)

ferroelectricchannel

Vgate

x- rays, light

substrate

PTC

♦ Hystereticmodulation of the

charge density in a

magnetic channel

♦ Low screeninglength⇒ study and control interface

magnetism

27

Multiferroic tunnel barrier

La0.1Bi0.9MnO3 tunnel barriers

a) Ferromagnetic insulator: spin filtering

b) ferroelectric: barrier profile depends on P direction Magnetic and electric control of a tunnel current

M. Gajek et al., Nature Mat. 6, 296 (07)

28

Applications

• Microwave applications:

transducer H(ω) → E(ω)

electromechanical: 100 kHz, magnetic resonances: 10 – 100 GHz

• Magnetic field sensors (free-standing laminar composites)

• Suggested: magnetoelectric electronics

(Electric control of magnetization in memories, logical circuits, ..)

16 Mbit MRAM (IBM, Infineon)

Si

MOS-FET SQUID






Summary, Literature

29

Second harmonic generation (SHG)

Electric field in matter: E(w) = E0eiωt(Incident light wave: frequency, direction, amplitude, polarization)P(ω) = ε0 χ E(ω) ~ eiωtLinear approximation only for weak (light) fields

For strong electromagnetic fields (e.g. laser):P = ε0 ( χ(1) E + χ(2) E E + χ(3) E E E + ... )with leading-order nonlinear term:P(2ω) = ε0 χ(2) E(ω) E(ω) ~ ei2ωt→ Frequency doubling ("second harmonic generation", SHG)

∑ ω−−ω−−⟩⟩⟨⟩⟨⟨∝χ i gigf EEEE greiireffreg ))(2( ||||||)2( hh rrr

E(ω)

E(ω)

P (2ω)

E x c i t e d s t a t e

G r o u n d s t a t e

Intermedi-ate states

⟨ | f

⟨ | i

⟨ |g

Microscopically:second-order perturbationM. Fiebig, thesis (Universität Dortmund, 1996)

30

Second harmonic generation (SHG)

SHG: Si(2ωωωω) ∝∝∝∝ χχχχijk Ej(ωωωω) Ek(ωωωω)Scr Smag

1.8 2.0 2.2 2.4 2.6 2.8 3.00

T = 10 K

crystallog.magnetic

SH

inte

nsity

SH energy (eV)

Cr2O3

χχχχijk ↔↔↔↔ symmetry ↔crystallographic and magneticstructure (Note: the higher the

symmetry the more χijk = 0) Spectroscopy : sublatticeselective excitation Spatial resolution: imagingof domain structures

M. Fiebig, thesis (Universität Dortmund, 1996)

Simultaneous access to magnetic

and ferroelectric order / domains!

31

Second harmonic generation

Non-vanishing χyyy:

Mn excitation for this

particular triangular structure2.2 2.4 2.6 2.8 3.0 3.2

0

20 40 60 8005Γ1→5Γ2S

H in

tens

ity

SH energy (eV)

χyyy

T

N

2.46 eV

Temperature (K)

YMnO3

295 KPol. σ+

1 mm

Antiferromagnetic 180°domains

Cr2O3

Antiferromagnetic domains,

contrast depends on

(circular) light polarization

M. Fiebig, PRL 1996, and further references years 2000 -05

32

Direct strain on piezoelectric substrates

J.-P. Locquet et al., Nature 394, 453 (1998)

Find strain-sensitive materials

33


In-situ strain:

•••• biaxial, uniform

•••• reversible

C. Thiele, K. D. at el., APL 87, 262502 (05) M. Bieg alsky, H. M. Christen, K. D. (2007)

piezo - crystal

conducting film

Vpiezo

IVI > 0V = 0PMN-PT(001)

72Pb(Mg1/3Nb2/3)O3 – 28PbTiO 3

rhombohedral, a = 4.02 Å

αααα = 89.90o

cf. LaAlO 3: αααα = 89.93o

92 94 96 98 100 102

103

104

105

106 V = 300 V V = 0

Inte

nsity

(a.

u.)

2 Theta (degree)

MgO 004

PMN-PT 004

33a


C. Thiele, K. D. at el., APL 87, 262502 (05)

piezo - crystal

conducting film

Vpiezo

IVI > 0V = 0PMN-PT(001)

72Pb(Mg1/3Nb2/3)O3 – 28PbTiO 3

rhombohedral, a = 4.02 Å

αααα = 89.90o

cf. LaAlO 3: αααα = 89.93o

In-situ strain:

•••• biaxial, uniform

•••• reversible

175 200 225 250 275 3000

2

4

6

0

100

200

300

400

resi

stan

ce

(kΩΩ ΩΩ

)

temperature (K)

δεδεδεδεxx = - 0.12 %

gaug

e fa

ctor

δεδεδεδεxx = 0

La0.8Ca0.2MnO3/PMN-PT(001)

34

Summary

Magnetoelectric multiferroics:

♦ joined magnetic and electric polarizibility in one material

♦ Most single-phase compounds for basic research (low T -apart from BiFeO3, low magnitude of ME effect)

♦ Composites for application (large ME effect at RT, mostlystrain-coupled)

Outlook:

♦ Understanding spiral magnetoelectricity

♦ Toroidal domains

♦ Little work on dynamic properties

♦ Stable magnetoelectric switching at 300 K

♦ Superlattices for “unconventional optics“

♦ Charge effects (e. g., field effect) at interfaces

35

Literature

Recent reviews :

M. Fiebig: Revival of the magnetoelectric effect, J. Phys. D 38, R123 (2005)

W. Prellier, M. P. Singh, P. Murugavel: The single-phasemultiferroic oxides – from bulk to thin film, J. Phys.: Cond. Matter 17, R803 (2005)

N. A. Spaldin, M. Fiebig: The renaissance of magnetoelectric multiferroics, Science 309, 391 (2005)

W. Eerenstein, N. D. Mathur, J. Scott: Multiferroic and magnetoelectric materials, Nature 442, 759 (2006)

D. I. Khomskii: Multiferroics – different ways to combinemagnetism and ferroelectricity, J. Magn. Magn. Mater. 306, 1 (2006)

*Proceedings of the MEIPIC conferences

Magnetoelectric Multiferroics - MAGNETISM.eumagnetism.eu/esm/2007-cluj/slides/doerr1-slides.pdfMagnetoelectric Multiferroics Kathrin Dörr, ... Faraday rotation ... good elastic coupling

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