Combining ferroelectricity and magnetism: the low … ferroelectricity and magnetism: the low energy electrodynamics Diyar Talbayev Center for Integrated Nanotechnologies Los Alamos

Combining ferroelectricity and magnetism: the Combining ferroelectricity and magnetism: the low energy electrodynamicslow energy electrodynamics

Diyar TalbayevDiyar TalbayevDiyar TalbayevDiyar TalbayevCenter for Integrated NanotechnologiesCenter for Integrated Nanotechnologies

Los Alamos National LaboratoryLos Alamos National Laboratory

Toni TaylorToni TaylorA.V. BalatskyA.V. BalatskyDarryl SmithDarryl SmithStuart TrugmanStuart TrugmanJohn O’HaraJohn O’Hara

Los Alamos National LaboratoryLos Alamos National Laboratory Osaka University, JapanOsaka University, Japan

Tsuyoshi KimuraTsuyoshi Kimura

AcknowledgementsAcknowledgements

Rick AverittRick Averitt

Boston UniversityBoston University

Inha University, KoreaInha University, Korea

Namjung HurNamjung Hur

Nanyang Technological Nanyang Technological University, SingaporeUniversity, Singapore

Andrew LaforgeAndrew LaforgeDmitri BasovDmitri Basov

UCSDUCSD

Funding provided by the Los Alamos National Laboratory Directed Research and Development Program

Rick AverittRick Averitt University, SingaporeUniversity, Singapore

Elbert ChiaElbert ChiaRutgers UniversityRutgers University

Seongsu LeeSeongsu LeeS.S.--W. CheongW. Cheong

Ferroic propertiesFerroic properties

FERROMAGNETISMFERROELECTRICITY

High-power current-driven write operation

Low-power voltage-driven write

But…

Issues of fatigue need to be overcome

… enter MULTIFERROICITY!!!

Magnetoelectric multiferroicsMagnetoelectric multiferroics

MULTIFERROICS – materials with coexisting

magnetism and ferroelectricity.

Magnetic order Electric polar ization

magnetoelectric interaction

Possible applications for magnetoelectric materials

Magnetoelectric memoryMagnetically switched electro-optic deviceElectric-field-modulated visible Faraday rotatorMagnetically (electrically)-modulated piezoelectric (piezomagnetic) devices, etc.

V. E. Wood, A. F. Austin, Int. J. Magnetism 5, 303-315 (1974)

Magnetoelectric effectMagnetoelectric effect

BiFeO 3 : ferroelectric antiferromagnet

Bi

Turn the magnetic moments!

Apply electric fieldE

Fe ions:

OFe

Y.-H. Chu et al.,

Nat. Materials 7 478 (2008)

moments!

Top view

easy axis for magnetization

Dynamic magnetoelectric effectDynamic magnetoelectric effect

BiFeO 3

Bi

OFe

Top view

PM

Rock the polarization

excite phonons

Magnetic

Y.-H. Chu et al.,

Nat. Materials 7 478 (2008)

Magnetic moments respond!

DYNAMIC MAGNETOELECTRIC EFFECTMixing of magnetic and lattice vibrations –

Magnetic and lattice motion interacts with lightMagnetic and lattice motion interacts with light

Electromagnetic wave incident on the crystal

??

Phonons ~ oscillating electric dipole

�� Coupling to the electric field of the light wave

Phonons in BiFeO 3

Lobo et al.,

Phys. Rev. B 76

172105 (2007)

33 cm -1 ~ 1 THz ~ 4 meV �� Resonance in the dielectric function, a.k.a. optical conductivity:

ε(ω)ε(ω)ε(ω)ε(ω) σ(ω)σ(ω)σ(ω)σ(ω)

Magnetic and lattice motion interacts with lightMagnetic and lattice motion interacts with light

Electromagnetic wave incident on the crystal

Magnetic excitations in BiFeO 3

0.8

33 cm -1 ~ 1 THz ~ 4 meV

Magnons ~ oscillating magnetic dipole

�� Coupling to the magnetic field of the light wave

10 15 20 25 30 350.0

0.2

0.4

0.6

Tra

nsm

issi

on

Frequency (cm -1)

T=30 K

33 cm -1 ~ 1 THz ~ 4 meV

D. Talbayev et al.,

unpublished

light wave

�� Resonance in the magnetic susceptibility:

χ(ω)χ(ω)χ(ω)χ(ω) µ(ω)µ(ω)µ(ω)µ(ω)

Mix it up: electromagnonsMix it up: electromagnons

TbMn2O5 : antiferromagnet and ferroelectric

Sushkov et al, Phys. Rev. Lett. 98 27202 (2007)

electric dipole active magnon : electro magnon

Similar observations : multiferroics TbMnO 3, Eu0.75Y0.25MnO3

Pimenov et al., Nature Phys. 2 97 (2006)

Valdes Aguilar et al., Phys. Rev. B 76 060404R (2007)

Pimenov et al., Phys. Rev. B 77 014438 (2008)

Electromagnons determine magnetoelectric functionalityElectromagnons determine magnetoelectric functionality

Sushkov et al, Phys. Rev. Lett. 98 27202 (2007)

TbMn2O5 : antiferromagnet and ferroelectric

antiferromagnet, ferroelectric

paramagnet

onset of electromagnon response

i)i) Properties of electromagnons Properties of electromagnons depend on the microscopic ME depend on the microscopic ME

ferroelectric

∫∞

+=0

21

1 810 ωω

ωσε d)(

)(Electromagnon contributes to static dielectric constant:

(i)

Electromagnon properties depend on the microscopic magnetoelectric coupling

(ii)

Dynamic magnetoelectric effect in hexagonal BaDynamic magnetoelectric effect in hexagonal Ba0.60.6SrSr1.41.4ZnZn22FeFe1212OO2222

Layered magnetic structure Several magnetic phases

N. Momozawa and Y. Yamaguchi,

J. Phys. Soc. Jpn. 62 12992 (1993)T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)

Dynamic magnetoelectric effect in hexagonal BaDynamic magnetoelectric effect in hexagonal Ba0.60.6SrSr1.41.4ZnZn22FeFe1212OO2222

Control of electric polarization by magnetic field:

T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)

Electrons, phonons, magnons

visible optical pulse excitation, a.k.a. pump

TimeTime--domain studies of elementary excitationsdomain studies of elementary excitations

Pump and probe wavelength: 800 nm (~1.5 eV)

optical pulse interrogation (probe) of material’s response

Dynamics of photo-excited quasiparticles often expo ses properties not detected by conventional probes – transport, magneti zation, or optical

conductivity

TimeTime--domain detection of magnetic motiondomain detection of magnetic motionMagneto-optical Kerr effect (MOKE) – rotation of pol arization of light

upon reflection by a magnetized medium

reflected probe beam

MO

KE

inte

nsity

ferromagnet

La2/3Ca1/3MnO3

M

D. Talbayev et al, Phys. Rev. B 73 14417 (2006); Appl. Phys. Lett. 86 182501 (2005)

0 500 1000

MO

KE

inte

nsity

Time (ps)arrival of pump

effHMM ×−= γ&demaganisotropyeff HHHH ++= 0

20

40

60

80

1.5 T

1.0 T

0.5 T

0.1 T

R/R

(x1

0-6)

0 Tpump

probe

c axis

TimeTime--resolved reflectance : coherent responseresolved reflectance : coherent response

BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO2222 : photoinduced change in : photoinduced change in reflectancereflectance

Coherent excitation of Coherent excitation of magnetic or lattice motionmagnetic or lattice motion

0 50 100 150 200 250-20

0

20

2.5 T

2.0 T∆R

/R (

x10

Time (ps)

T=10 K400-nm pump and probe

B

D. Talbayev et al., Phys. Rev. Lett. 101 097603 (2008)

magnetic or lattice motionmagnetic or lattice motion

20

30

40

50

60

field normal to the c axis field along the c axis

10

20

30

40

50

Osc

illat

ion

freq

uenc

y (G

Hz)

ocsillation frequency ω

Magnetic or lattice?Magnetic or lattice?

0.0 0.5 1.0 1.5 2.0

10

Magnetic field (T)

T=10 K0

10 Osc

illat

ion

freq

uenc

y (G

Hz)

N. Momozawa and Y. Yamaguchi, J. Phys. Soc. Jpn. 62 12992 (1993)


Strong evidence in support of magnetic origin of th e excitation – electron spin resonance, i.e., k=0 magnon

λ/nfPHONONS ∝

Oscillation frequency:

More evidence against the latticeMore evidence against the lattice

∆R/R

(ar

b. u

nits

)

T=15 KH=0.2 T

400 nm

800 nm

LuMnO3

D. Lim et al., Appl. Phys. Lett. 83 4800 (2003)

0 50 100 150 200

(∆R/R(800)-decay) x 10

∆

Time (ps)


Identical oscillation frequency at different probe wavelengths

Calculation of magnon frequenciesCalculation of magnon frequencies

N. Momozawa and Y. Yamaguchi,J. Phys. Soc. Jpn. 62 12992 (1993)

B

∑ ++⋅⋅⋅= )();;( 222121 SizLizSSLLLjSiex MMDMMMMMMHH

D – the only free parameter

T. Kimura, G. Lawes, and A.P. Ramirez, PRL 94 137201 (2005)

Calculation of magnon frequenciesCalculation of magnon frequencies


40

60

80

1.5 T

0.5 T

R

/R (

x10-6

)

0 T

Dynamic magnetoelectric effectDynamic magnetoelectric effect

BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO2222

2

1

1

+−=

n

nR

ε=n

Modulation of reflectance

Modulation of n and εεεε

0 50 100 150 200 2500

201.5 T∆R

/R (

x10

Time (ps)


Modulation of n and εεεεby magnon motion: dynamic magnetoelectric effect

Optical detection of magnetic state using reflectio n –implications for data storage and spintronics.

Tc=875 K

PFE

Magnetoelectricity in hexagonal HoMnOMagnetoelectricity in hexagonal HoMnO33

Ferroelectric

z=0z=c/2

40 K < T < 72 KTR TN

Mn ions:

Triangular antiferromagnet, TN=72 K

Litvinchuk et al., JPCM 16 809 (2004)

z=0

z=c/2

Vajk et al., PRL 94 87601 (2005)

5 K < T < 40 K

T < 5 K

THo

TRTHo

Two sites: Ho(1) C3v

Ho(2) C3 – ordered for T<THo=5 K

z

Magnetoelectricity in hexagonal HoMnOMagnetoelectricity in hexagonal HoMnO33

Magnetism of Ho 3+

(S=2, L=6, J=8) ions:

T<TN E=0

Mag

netiz

atio

n

Applied electric field induces magnetization of Ho ions:

Hint=ΣSHoΑSMn

Lottermoser et al., Nature 430 541 (2004)

Mag

netiz

atio

n

(110)

c (001)

||h||H

static field

FarFar--infrared study of magnetic excitationsinfrared study of magnetic excitations

HoMnO3

⊥h⊥H

lightwave

3 6 9 12 15

-0.5

0.0

0.5

1.0

E fi

eld

ampl

itude

Time (ps)

SAMPLE REFERENCE

1 THz � 300 µm � 0.004 eV �33cm-1 � 47 K

FarFar--infrared study of magnetic excitationsinfrared study of magnetic excitations

gating pulse

excitation pulse

Time (ps)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20

25

E fi

eld

ampl

itude

Frequency (THz)

SAMPLE REFERENCE

gating pulse

• Broadband• Measurement of electric field E

(1) Photoconductive antennas

(2) Electro-optic crystals

||h

⊥h

Magnetic excitations in HoMnOMagnetic excitations in HoMnO33

0.10

0.15

0.20

0.25

0.30

Tra

nsm

issi

on h || c

T=10 K

20 30 40 50 60 70 80 90 1000.00

0.05

Frequency (cm-1)

h | c

�� Crystal field excitations of Ho ions

�� Antiferromagnetic resonance (AFMR) of Mn ions

Neutron scattering: Vajk et al., Phys. Rev. Lett. 94 87601 (2005)

Two Ho 3+ (S=2, L=6, J=8) cites with C3 and C3v point symmetries

Crystal field splitting of HoCrystal field splitting of Ho3+3+ ground stateground state

J=8

06 ,s

428 m,,±±

a6

06 ,s

7±

8±m = -8..+8

Abragam and Bleaney, Electron paramagnetic resonance of transition ions, Clarendon press, 1970

333 −+=s

517 m,,±±

333 −−=a

06 ,s

1±

0

The electrostatic environment of Ho ions determines the crystal field splitting

Magnetic resonance of Mn ionsMagnetic resonance of Mn ions

M3

M2

M1

z

∑2

λ

B

B

Classical treatment

ji MMF ⋅Σ= λ zi

zi MBMK Σ−+ ∑

2)(

Interaction parameters measured by neutron scatteri ng in zero field by Vajk et al., Phys. Rev. Lett. 94 8760 1 (2005)


40

50

60

70

80

90

40

50

60

70

80

90

40

50

60

70

80

90

T=10 K, B || c

Fre

quen

cy (

cm-1)

T=10 K, B | c

20

30

40

0 1 2 3 4 5 6 7 820

30

40

0 1 2 3 4 5 6 7 820

30

40

Magnetic field (T)

Fre

quen

cy (

cm

Magnetic field (T)



0MH ex λ=0KMH d =


0KMH d =Palme et al., Solid State Comm. 76 873 (1990)

Why the discrepancy?

Exchange coupling between Ho and Mn ionsExchange coupling between Ho and Mn ions

Penney et al., J. Appl. Phys. 40 1234 (1969)

YMnO3: similar material – hexagonal lattice, ferroelectri c, triangular antiferromagnet … but Y ions are not magn etic

…and the calculation works!!

Sato et al., Phys. Rev. B 68 014432 (2003)

Discrepancy in HoMnO 3 is due to Ho-Mn (HM) exchange interaction:

MnMnHoHM Bχ== ~

Effective magnetic field acting on Mn ions!

Mnz

Bzz

Mnjz

Hoizij

HMex S

g

BJSSJH

µχ== ~

1−=HMλ∑∑ == MnizHM

Mniz

Bz

zHM MBMB

gg

JF λ

µχ

2

6


Magnetoelectricity in HoMnOMagnetoelectricity in HoMnO33

Ferromagnetic exchange between Ho and Mn:

Mnjz

Hoiz

zij

HMex SSJH

~= 0~ <z

ijJ

Same interaction responsible for the magnetoelectri city:T<TN E

Mag

netiz

atio

n

Lottermoser et al., Nature 430 541 (2004)

Mag

netiz

atio

nMagnons allow the determination of microscopic

details of magnetoelectric interaction.

In HoMnO 3, it is the Ho-Mn magnetic exchange coupling.

SummarySummary

Magnetic and lattice excitations (magnons and phono ns) play a fundamental role in the quest for understand ing and exploiting magnetoelectric materials

(i)

Detection of magnetic motion and magnetic state via the modulation of reflectance

(ii)

0.5 T

∆R/R

(x1

0-6)

BaBa0.60.6SrSr 1.41.4ZnZn22FeFe1212OO22

22

0 50 100 150 200Time (ps)


Properties of magnons and phonons help reveal the microscopic details of magnetoelectric interaction

(iii)

Mnjz

Hoiz

zij

HMex SSJH

~=

HoMnO3

Documents

Combining ferroelectricity and magnetism: the low … ferroelectricity and magnetism: the low energy electrodynamics Diyar Talbayev Center for Integrated Nanotechnologies Los Alamos