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...
TRANSCRIPT
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)
Phase Coexistence & Spin Topography (ScMnO3)
2.1 2.2 2.3 2.4 2.5 2.6 2.70
6T = 1.5 K
|χxxx|2
|χyyy|2
SH energy (eV)
SH in
tens
ity
2.1 2.2 2.3 2.4 2.5 2.6 2.70
6mmT = 1.5 K
|χxxx|2
|χyyy|2
SH energy (eV)
SH in
tens
ity
ϕspin (x axis = 0°)0
102030405060708090
2.1 2.2 2.3 2.4 2.5 2.6 2.70
P63cmT = 1.5 K
|χxxx|2
|χyyy|2
SH energy (eV)
SH in
tens
ity
χxxx
Spin - angle topography
1.0 mm
χyyy
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
Antiferromagnetic domains
⊗ ⇒
⊗ ⇒
⊗ ⇒
+ −
+
−
−
+ −
+
+ −
+
−
−
+ −
+
−
+ −
++ −
+ −
−
+ −
+
Ferroelectromagnetic Domains
0,5
mm
Model
Experiment
Ferroelectric domains
Ferroelectromagnetic domains
Antiferromagnetic domains
Ferroelectric domains
Ferroelectromagnetic domains
Antiferromagnetic domains
+ −
+
−
−
+ −
+
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