Part IV – Multiferroic RMnO3 - UCSB...SH = 2.52 eV 0 10 20 30 40 50 60 70 80 0 0 o 60 o 120 o 180...

Part IV – Multiferroic RMnO3

• Ferroelectric & magnetic ordering• SHG spectroscopy• SHG topography• Identification of multiferroic interactions

Multiferroic Hexagonal Manganites RMnO3

Hexagonal manganites RMnO3 (R = Sc, Y, In, Dy, Ho, Er, Tm, Yb, Lu)

T < TC ≈ 600-1000 K ⇒ ferroelectric (FEL) + paramagnetic (PM)

T < TN ≈ 65-130 K ⇒ ferroelectric (FEL) + antiferromagnetic (AFM)

T < TRE ≈ 5 K ⇒ FM or AFM order of R3+-spins for R = Ho - Yb

Ferroelectric order of RMnO3

B.B

. van

Ake

n, N

atur

e M

ater

. 3, 1

64 (2

004)

PEL

R 3+

Mn3+

O 2-

z

x

FELFerroelectric phase transition at TC ≈ 900 K

Breaking of inversion symmetry I

PG: 6/mmm → 6mm

Order parameter P ↔ ferroelectric polarization P = (0, 0, Pz)

Ferroelectric SHG contributions

Point group 6mm → broken inversion symmetry → ED-SHG

⇒ zCijkzCEDijk TTTT P)()( >=< χχ

Allowed components of χED: χzzz, χxxz(3) = χyyz(3)

( )

++∝

)()()()()()()(

)(ωχωωχ

ωωχωωχ

ω222

22

2

zzzzyxzxx

zyxxz

zxxxz

EEEEEEE

P

⇒

No SHG for k||z!

Ferroelectric SHG contributions

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00

10

0

1

0

1

0°

60°120°

180°

240° 300°

Pz ∝ ExEx

SH-energy (eV)

Pz ∝ EzEz

SH-in

tens

ity

YMnO3

T = 6 Kk || y

Px ∝ ExEz

|| x

|| zϕ

( )

++∝

)()()()()()()(

)(ωχωωχ

ωωχωωχ

ω222

22

2

zzzzyxzxx

zyxxz

zxxxz

EEEEEEE

P

• All expected SH contributions detectible

• Leading contribution χzxx

• No dependence on the R-ion

Antiferromagnetic order of RMnO3

In-plane triangular spin structure

⇒ geometric frustration

⇒ 120°-spin structure

+ inter-plane ordering

+ sublattice interaction Mn ↔ R

⇒ complex magnetic system!

Antiferromagnetic α- and β-order

Mn-Ion at z = 0Mn-Ion at z = c/2

• Ferromagnetic interplane coupling

• Spin lattice is inversion symmetric

• Antiferromagnetic interplane coupling

• Spin lattice is not inversion symmetric

α and β structures not distinguishable with diffraction techniques!

Anitferromagnetic α-order

ϕ

x

y

Mn-Ion bei z = 0Mn-Ion bei z = c/2

Three different spin-orders depending on the spin-angle ϕ distinguishable:

αx (ϕ=0°): PG 6mmED: -χyyy=χyxx=χxxy=χxyx

αy (ϕ=90°): PG 6mmED: -χxxx=χxyy=χyxy=χyyx

αϕ (ϕ=0°…90°): PG 6ED: αx ⊕ αy

Spin order distinguishable by SHG polarization!

Anitferromagnetic β-order

x

y

Mn-Ion bei z = 0Mn-Ion bei z = c/2

Three different spin-orders depending on the spin-angle ϕ distinguishable:

βx (ϕ=0°): PG 6mmED: χxyz=χxzy=-χyxz=-χyzx

βy (ϕ=90°): PG 6mmED: χzzz, χxxz(3) = χyyz(3)

βϕ (ϕ=0°…90°): PG 6ED: βx ⊕ βy

No SHG for k||z!

Magnetic Structure and SHG Selection RulesAt least 8 different in-plane spinstructures with different symmetries anddifferent selection rules for SHG

α structures β structuresx

y

6mm : Ex(ω) → Px(2ω) ~ χxxx

6mm : Ex(ω) → Py(2ω) ~ χyyy

6 : Ex(ω) → Px(2ω) ⊕Py(2ω)

6 . . : Ex(ω) → 0

etc.

Polarization of ingoing andoutgoing light reveals themagnetic symmetry

Pi(2ω) ∝ χijk Ej(ω)Ek(ω)6mm

6

6mm

6mm

6

6mm3m

3m

Symmetry determination by SHG spectroscopy

1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0

0

0

60120

180

240 300

0

60120

180

240 300

×3 ×1

×3 ×1 ErMnO3

Px ∝ ExEx

SH-energy (eV)

k || zT = 6 K

YMnO3

Py ∝ EyEy

2.46 eV

SH-in

tens

ity

TN

|| y

|| xϕ

20 800

T (K)

TN

2.56 eV

|| y

ϕ|| x

αx order

αy order

y polarized SHG 6mm ∝ |χyyy|2

x polarized SHG 6mm ∝ |χxxx|2

Symmetry determination by SHG spectroscopyx-component of P(2ω)⇒ Symmetry 6mm

2.0 2.2 2.4 2.6 2.8 3.00

2.0 2.2 2.4 2.6 2.8 3.0

0

0

0

0

0

0

70 K

SHG-energy (eV)

Lu

SHG

-inte

nsity

6 KLu

6 KY

6 KY

6 KEr

6 KEr

6 KHo

50 KHo

1.5 KSc

1.5 KSc

5 KTm

5 KTm

5 KYb

5 KYb

y-component of P(2ω)⇒ Symmetry 6mm Spin || x-axis (Symmetry 6mm)

⇒ Intensity maximum at 2.46 eV

Spin || y-axis (Symmetry 6mm)

⇒ Intensity minimum at 2.46 eV

Just by using the spectraldegree of freedom the magneticsymmetry can be determined!

Phase Transitions in RMnO3 (R = Sc, Ho, Lu)

χxxx

ESH = 2.52 eV

0 10 20 30 40 50 60 70 800

0o

60o

120o

180o240o

300o

0o

60o

120o

180o240o

300o

χyyy

TNTRSH

inte

nsity

Temperature (K)

χxxx

ESH = 2.44 eV0 20 40 60 80 100 120 140

0

0o

60o

120o

180o240o

300o0o

60o

120o

180o240o

300o

χyyy

TN

SH in

tens

ity

Temperature (K)

ESH = 2.47 eV

χxxx

ESH = 2.44 eV

0 10 20 30 40 50 60 70 80 900

0o

60o

120o

180o240o

300o

0o

60o

120o

180o240o

300o χyyy

TN

SH in

tens

ity

Temperature (K)

ScMnO3

HoMnO3

LuMnO3

Temperature depended change of symmetry:

High T: 6mm

Low T: 6mm

In addition temperature ranges with coexisting phases and reduced symmetry!

Phase Coexistence in ScMnO3

0 20 40 60 80 100 1200

TN6mm6

Temperature (K)

SHG

-inte

nsity xxx yyy

66mm

6mm

Temperature depended Spatial resolved

Geometric Model for Spin-Angle Calculation

From symmetry: PG ϕspin χxxx χyyy

6mm 0° 0 ≠0

6mm 90° ≠0 0

6 0°…90° ≠0 ≠0

Geometric model: Calculating spin-angle from SHG intensities

χxxx(ϕspin)=χ0xxxsin(ϕspin)

χyyy(ϕspin)=χ0yyycos(ϕspin)

Spin Rotation in HoMnO3

Phase transition at ≈41 K:

T < TR: Symmetry 6mm

T > TR: Symmetry 6mm

⇒ 90° spin rotation at TR = 41 K

1.0 mm

xy

ϕ

0 10 20 30 40 50 60 70 800

TN

~ χxxx

~ χyyy

SH in

tens

ity

Temperature (K)

Spin-Rotation Domains in HoMnO3

Inside AFM domain walls reduced local symmetry 2 due to uncompensated magnetic moment.

2 allows ME contribution Pz ∝ αzx,y Mx,y

⇒ Local ME effect

ϕx

Sx∼ Iy

y

Sy∼ Ix

0.5

0.5S

0

0 20 40 60 0 20 40 60

0 1 2 3 4 50

0 1 2 3 4 5

Ix

(b)(a)

TN

Temperature (K)

SH in

tens

ity

0 T

P63cm

Iy

Temperature (K)

0 T

P63cm

Magnetic field (T)

(d)(c)

SH in

tens

ity

20 K

Magnetic field (T)

20 K

ϕx

Sx∼ Iy

y

Sy∼ Ix

0.5

0.5Sϕ

x

Sx∼ Iy

y

Sy∼ Ix

0.5

0.5Sϕ

x

Sx∼ Iy

y

Sy∼ Ix

0.5

0.5S

0

0 20 40 60 0 20 40 60

0 1 2 3 4 50

0 1 2 3 4 5

Ix

(b)(a)

TN

Temperature (K)

SH in

tens

ity

0 T

P63cm

Iy

Temperature (K)

0 T

P63cm

Magnetic field (T)

(d)(c)

SH in

tens

ity

20 K

Magnetic field (T)

20 K

6mm 6mm

6 66mm

Magnetic Phase Diagram of Hexagonal RMnO3

Sc In Lu Yb Tm Er Ho Y6.155 Å5.833 Å In-plane lattice constant

Tem

pera

ture

(K)

20

40

60

80

100

120RMnO3

αx (P 63cm)αρ (P 63) αy (P 63cm)

αx (6mm)αϕ (6)αy (6mm)

Magnetic Phase Diagram of ErMnO3

0

10

20

30

40

50

60

70

80

0 1 2 3 4

6mm

TN(Mn) paramagnetic

6mm

-- or --

6mm

6mm

Magnetic field (T)

Tem

pera

ture

(K)

Reorientation of Mn3+ sublattice inmagnetic field along hexagonal axis

Phys. Rev. Lett. 88, 027203 (2002)

Magnetoelectric effect:forbidden allowed

0

0 1 2 3 4

50 K

Magnetic field (T)

SH in

tens

ityMagnetic field0 T

α-order β-order6mm3m6mm

H/T Phase Diagram of Hexagonal RMnO3

0 1 2 3 40

10

20

30

40

50

60

70

80

TmMnO3

A2

B2

Tem

pera

ture

(K)

Magnetic field µ0Hz (T)

ErMnO3

A2

B2

0

10

20

30

40

50

60

70

80

HoMnO3

A1

B2

A2B1

Tem

pera

ture

(K)

0 1 2 3 4

YbMnO3

B2

A2

Magnetic field µ0Hz (T)

Sc In Lu Yb Tm Er Ho Y

Tem

pera

ture

(K)

0

20

40

60

80

100

120

140

RMnO3 (H = 0) (none)(hyst.)

2

1B

A

Repres. indexRepresentation

J. A

ppl.

Phys

. 83,

819

4 (2

003)

ME effectallowed

6mm (αy) 6mm (βx)

6mm (αx) 6mm (βy)

T

H

ME effectforbidden

αy

αy

αyαy

βyαx

βx

βx

βx

βx

α

β

x

yx/y

So far…

• Detection of obviously FEL/AFM induced SHG

• Analysis of magnetic ordering

• Phase diagrams depending on temperature & magnetic field

But what about the multiferroic nature of RMnO3?

SHG in a Multiferroic Compound

[ ] )()(...)(ˆ)(ˆ)(ˆ)0(ˆ)2( 0 ωω+℘χ+χ+℘χ+χε=ω EEPNL

χ(0): Paraelectric paramagnetic contribution always allowedχ(P ): Ferroelectric contribution allowed belowχ( ): Antiferromagnetic contribution the respectiveχ(P ): Ferroelectromagnetic contribution ordering temperature

ED contribution for magnetic ferroelectrics:

Analog for MD and EQ ⇒ in total 12 possible contributions!

But later ones only taken into account if ED not allowed.

Symmetry analysis

OrderedSublattice

Point group

Parity - typesymmetry operation

Order parameter

(para) 6/mmm I, T, IT ---FEL 6mm T P

AFM 6/mmm I

FEL + AFM 6mm --- P

• Only αx order taken into account • FEL, AFM & FEL+AFM as separated sublattices

x

y

SHG contributions

k || xSy 2i1EyEz --- --- e1Ey

2

Sz i2Ey2 + i3Ez

2 --- --- ---

k || ySx 2i1ExEz --- -2q1ExEz ---Sz i2Ex

2 + i3Ez2 m1Ex

2 -q2Ex2 ---

k || zSx --- -2m1ExEy -2q3ExEy -2e1ExEy

Sy --- m1(Ey2 – Ex

2) q3(Ey2 – Ex

2) e1(Ey2 – Ex

2)

Lowest order non-zero contributions to SHG:

Zero order: Electric dipole (ED): and

First order: Magnetic dipole (MD):

First order: Electric quadrupole (EQ):

321 iiiED ,,)(ˆ =Pχ 1eED =⋅ )(ˆ Pχ

1mMD =)(ˆ χ

321 qqqEQ ,,)(ˆ =χ

Magnetoelectric SHG

Identical magnetic spectrafor k||z and k||x indicatebilinear coupling to P, .

Unarbitrary evidence forthe observation of"magnetoelectric SHG"

2.0 2.2 2.4 2.6 2.82.0 2.2 2.4 2.6 2.80

×10

χyyy

×1

χyyy

χzzz

χyyz

χzyy

×10

×2500

SH energy (eV)

k || z k || x

SH in

tens

ity

SH energy (eV)

Source term SED(P) SMD,EQ() SED(P)Sublattice sym. 6mm 6/mmm 6mmSHG for k || z = 0 ≠ 0

≠ 0SHG for k || x ≠ 0 = 0

What about domains?Ferroelectric domains

Ferroelectromagnetic domains

Antiferromagnetic domains

Ferroelectric and ferroelectromagnetic SHG contribution allow three experiments:

Ferroelectric domains



⊗ ⇒

⊗ ⇒

⊗ ⇒

+ −

+

−

−

+ −

+

+ −

+

−

−

+ −

+

−

+ −

++ −

+ −

−

+ −

+

Ferroelectromagnetic Domains

0,5

mm

Model

Experiment







+ −

+

−

−

+ −

+

Clamping of Antiferromagnetic DomainsCoexisting domains in YMnO3:

Ferroelectric domains: ∝P

Antiferromagnetic domains: ∝

"Magnetoelectric" domains: ∝PP = +1 for P = ±1, = ±1

P = -1 for P = ±1, = 1

Any reversal of FEL order parameterclamped to reversal of the AFM orderparameter → local ME effect

Coexistence of "free" and "clamped"AFM walls

AFM

FEL

FEL&

AFM0.5

mm −+

+−

−−

++

free

clamped

E-Field induced ME effect

+

0 10 20 30 40 50 60 70 80 900

1

2

3

4 χxxx

χyyy

χxxx

χyyy

SH-In

tens

ity (a

.u.)

Temperature (K)

unpoled

poled

Applying an electric field(= ferroelectric poling) above themagnetic phase transitiontemperature leads to quenchingof the magnetic SHG signal!

Magnetic SHG image

unpoled poled

Transition from α to β order?

Magnetic Phase Control by Electric Field

Nat

ure

430,

541

(200

4)

6mm 6mm

Magnetic Phase Control by Electric Field

Electric field suppresses magnetic SHG and leads to additional field depended contribution to Faraday rotation

⇒ Induction of magnetic phase transition!

Summary

Nonlinear optics is based on symmetry: χijk ↔ symmetry ↔ structure

Simultaneous study of all ferroic structures with the same technique

Nonlinear optics on multiferroics:

Access to:

Electric-magnetic phase diagrams

Magnetoelectric interactions

Multiferroic domain topology

Ultrafast dynamics

Etc. etc.

AcknowledgementsBonn:

Manfred FiebigDennis MeierTim HoffmannAnne ZimmermannMichael MaringerTobias KordelChristian Wehrenfennig

Cologne:

Ladislav BohatýPetra Becker

Dortmund:

Dietmar FröhlichStefan LeuteMartin KneipCarsten DegenhardSenta KallenbachThorsten KieferMatthias MaatClaudia Reimpell

Russia:

Roman PisarevVictor Pavlov

Japan:

Kai Kohn

Part IV – Multiferroic RMnO3 - UCSB...SH = 2.52 eV 0 10 20 30 40 50 60 70 80 0 0 o 60 o 120 o 180...

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Transcript of Part IV – Multiferroic RMnO3 - UCSB...SH = 2.52 eV 0 10 20 30 40 50 60 70 80 0 0 o 60 o 120 o 180...