Part IV Multiferroic RMnO 3. Ferroelectric & magnetic ordering SHG spectroscopy SHG topography Identification of multiferroic interactions

Transcription

1 Part IV Multiferroic RMnO 3 Ferroelectric & magnetic ordering SHG spectroscopy SHG topography Identification of multiferroic interactions

2 Multiferroic Hexagonal Manganites RMnO 3 Hexagonal manganites RMnO 3 (R = Sc, Y, In, Dy, Ho, Er, Tm, Yb, Lu) T < T C 6-1 K ferroelectric (FEL) + paramagnetic (PM) T < T N K ferroelectric (FEL) + antiferromagnetic (AFM) T < T RE 5 K FM or AFM order of R 3+ -spins for R = Ho - Yb

3 Ferroelectric order of RMnO 3 PEL R 3+ FEL Ferroelectric phase transition at T C 9 K Mn 3+ O 2- z Breaking of inversion symmetry I PG: 6/mmm 6mm x B.B. van Aken, Nature Mater. 3, 164 (24) Order parameter P ferroelectric polarization P = (,, P z )

4 Ferroelectric SHG contributions Point group 6mm broken inversion symmetry ED-SHG z C ijkz C ED ijk T T T T P ) ( ) ( > = < χ χ Allowed components of χ ED : χ zzz, χ xxz (3) = χ yyz (3) ( ) + + ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ω χ ω ω χ ω ω χ ω ω χ ω z zzz y x zxx z y xxz z x xxz E E E E E E E P No SHG for k z!

5 Ferroelectric SHG contributions 1 P x E x E z YMnO 3 T = 6 K k y P ( 2ω ) χ zxx 2χ 2χ ( ω) E ( ω) E ( ω) ( ω) ( ) xxz y z E ( ω) + E ( ω) + χ E ( ω) x xxz E E x y z zzz z 1 SH-intensity P z E z E z All expected SH contributions detectible x 6 ϕ z 24 3 P z E E x x SH-energy (ev) Leading contribution χ zxx No dependence on the R-ion

6 Antiferromagnetic order of RMnO 3 In-plane triangular spin structure geometric frustration 12 -spin structure + inter-plane ordering + sublattice interaction Mn R complex magnetic system!

7 Antiferromagnetic α- and β-order Ferromagnetic interplane coupling Spin lattice is inversion symmetric Antiferromagnetic interplane coupling Spin lattice is not inversion symmetric Mn-Ion at z = Mn-Ion at z = c/2 α and β structures not distinguishable with diffraction techniques!

8 Anitferromagnetic α-order Three different spin-orders depending on the spin-angle ϕ distinguishable: ϕ α x (ϕ= ): PG 6mm ED: -χ yyy =χ yxx =χ xxy =χ xyx α y (ϕ=9 ): PG 6mm ED: -χ xxx =χ xyy =χ yxy =χ yyx Mn-Ion bei z = Mn-Ion bei z = c/2 y x α ϕ (ϕ= 9 ): PG 6 ED: α x α y Spin order distinguishable by SHG polarization!

9 Anitferromagnetic β-order Three different spin-orders depending on the spin-angle ϕ distinguishable: β x (ϕ= ): PG 6mm ED: χ xyz =χ xzy =-χ yxz =-χ yzx β y (ϕ=9 ): PG 6mm ED: χ zzz, χ xxz (3) = χ yyz (3) Mn-Ion bei z = Mn-Ion bei z = c/2 y x β ϕ (ϕ= 9 ): PG 6 ED: β x β y No SHG for k z!

10 Magnetic Structure and SHG Selection Rules At least 8 different in-plane spin structures with different symmetries and different selection rules for SHG 6mm 3m 6mm P i (2ω) χ ijk E j (ω)e k (ω) 6mm : E x (ω) P x (2ω) ~ χ xxx 6mm : E x (ω) P y (2ω) ~ χ yyy : E x (ω) P x (2ω) P y (2ω) 6.. : E x (ω) 6mm 3m 6mm etc. α structures y x β structures Polarization of ingoing and outgoing light reveals the magnetic symmetry

11 Symmetry determination by SHG spectroscopy 2.46 ev y 6 ϕ x YMnO 3 T = 6 K k z y polarized SHG 6mm χ yyy α x order SH-intensity T N 2.56 ev y 6 ϕ P y E y E y ErMnO 3 x polarized SHG 6mm χ xxx 2 18 x T N 2 8 T (K) 24 3 P x E x E x 1,6 1,8 2, 2,2 2,4 2,6 2,8 3, SH-energy (ev) α y order

12 Symmetry determination by SHG spectroscopy x-component of P(2ω) Symmetry 6mm Sc 1.5 K y-component of P(2ω) Symmetry 6mm Sc 1.5 K Spin x-axis (Symmetry 6mm) Intensity maximum at 2.46 ev Y 6 K Y 6 K Spin y-axis (Symmetry 6mm) Ho 5 K Ho 6 K Intensity minimum at 2.46 ev Er 6 K Er 6 K SHG-intensity Tm Yb Lu 5 K 5 K 7 K Tm Yb Lu 5 K 5 K 6 K Just by using the spectral degree of freedom the magnetic symmetry can be determined! SHG-energy (ev)

13 Phase Transitions in RMnO 3 (R = Sc, Ho, Lu) ScMnO 3 SH intensity HoMnO 3 SH intensity LuMnO 3 SH intensity 3 o 24 o o 6 o 12 o 18 o E SH = 2.52 ev T R χ xxx 3 o 24 o χ yyy o 6 o 12 o 18 o T N Temperature (K) χ xxx χ yyy o 6 o 3 o o 3 o 6 o 24 o 12 o 24 o 12 o 18 o 18 o E SH = 2.44 ev T N Temperature (K) o χ o χ xxx 3 o 6 o yyy E SH = 2.47 ev 24 o 3 o 6 o 12 o 18 o 24 o 12 o E SH = 2.44 ev 18 o T N Temperature (K) Temperature depended change of symmetry: High T: 6mm Low T: 6mm In addition temperature ranges with coexisting phases and reduced symmetry!

14 Phase Coexistence in ScMnO 3 Temperature depended Spatial resolved SHG-intensity 6 6mm T N xxx 6mm 6 yyy Temperature (K) 6mm

15 Geometric Model for Spin-Angle Calculation From symmetry: PG ϕ spin χ xxx χ yyy 6mm 6mm Geometric model: Calculating spin-angle from SHG intensities χ xxx (ϕ spin )=χ xxxsin(ϕ spin ) χ yyy (ϕ spin )=χ yyycos(ϕ spin )

16 Phase Coexistence & Spin Topography (ScMnO 3 ) χ xxx χ yyy 1. mm ϕ spin (x axis = ) Spin - angle topography P6 3 cm χ xxx 2 χ yyy 2 6mm χ xxx 2 χ yyy 2 6 χ xxx 2 χ yyy 2 SH intensity T = 1.5 K SH intensity T = 1.5 K SH intensity T = 1.5 K SH energy (ev) SH energy (ev) SH energy (ev)

17 Spin Rotation in HoMnO 3 SH intensity Temperature (K) ~ χ xxx ~ χ yyy T N Phase transition at 41 K: T < T R : Symmetry 6mm T > T R : Symmetry 6mm 9 spin rotation at T R = 41 K ϕ y x 1. mm

18 Spin-Rotation Domains in HoMnO 3 SH intensity Temperature (K) Temperature (K) T T (a) I y P6 6mm 3 cm (c) I x P6 6mm 3 cm T N (b) 2 K (d) 2 K SH intensity y S x I y.5 S.5 ϕ S y I x x Magnetic field (T) Magnetic field (T) 6 6mm 6 Inside AFM domain walls reduced local symmetry 2 due to uncompensated magnetic moment. 2 allows ME contribution P z α zx,y M x,y Local ME effect

19 Magnetic Phase Diagram of Hexagonal RMnO3 Temperature (K) RMnO 3 α x (P 6 cm) x (6mm) 3 α ρ (P 6 ) ϕ (6) 3 α y (P 6 cm) y (6mm) 3 Sc In Lu Yb Tm Er Ho Y Å In-plane lattice constant Å

20 Magnetic Phase Diagram of ErMnO 3 8 T N (Mn) paramagnetic Reorientation of Mn 3+ sublattice in magnetic field along hexagonal axis 7 6 6mm 6mm -- or -- T Magnetic field Temperature (K) SH intensity 6mm 6mm Magnetic field (T) Phys. Rev. Lett. 88, 2723 (22) Magnetic field (T) K 6mm 3m 6mm α-order β-order Magnetoelectric effect: forbidden allowed

21 H/T Phase Diagram of Hexagonal RMnO 3 Temperature (K) RMnO 3 (H = ) Representation αb (hyst.) βa Repres. index 1x (none) x/y 2y Sc In Lu Yb Tm Er Ho Y T 6mm (α y ) 6mm (β x ) Temperature (K) Temperature (K) HoMnO 3 βa x2 B A 2 Aβ α x1 β x 1y αb 2 y αb 2y βa 2x TmMnO Magnetic field µ H z (T) Bα 2y αb y 2 YbMnO 3 ErMnO 3 βa x Magnetic field µ H z (T) J. Appl. Phys. 83, 8194 (23) 6mm (α x ) 6mm (β y ) ME effect forbidden ME effect allowed H

22 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 RMnO 3?

23 SHG in a Multiferroic Compound ED contribution for magnetic ferroelectrics: P NL [ χˆ() + χˆ( ) + χˆ( ) + χˆ( ) +...] E( ω) E( ) ( 2ω) = ε ω χ(): Paraelectric paramagnetic contribution always allowed χ(p ): Ferroelectric contribution allowed below χ( ): Antiferromagnetic contribution the respective χ(p ): Ferroelectromagnetic contribution ordering temperature Analog for MD and EQ in total 12 possible contributions! But later ones only taken into account if ED not allowed.

24 Symmetry analysis Only α x order taken into account FEL, AFM & FEL+AFM as separated sublattices y x Ordered Sublattice Point group Parity - type symmetry operation Order parameter (para) 6/mmm I, T, IT --- FEL 6mm T P AFM 6/mmm I FEL + AFM 6mm --- P

25 SHG contributions Lowest order non-zero contributions to SHG: Zero order: Electric dipole (ED): First order: Magnetic dipole (MD): First order: Electric quadrupole (EQ): ED ED ˆ χ ( P ) = i, i, and ˆ χ ( P ) = e1 ˆ χ MD ( ) = EQ ˆ ( ) = χ 1 2 i3 m 1 q1, q2, q3 k x k y k z S y 2i 1 E y E z e 1 E y 2 S z i 2 E y2 + i 3 E z S x 2i 1 E x E z q 1 E x E z --- S z i 2 E x2 + i 3 E z 2 m 1 E x 2 -q 2 E x S x m 1 E x E y -2q 3 E x E y -2e 1 E x E y S y --- m 1 (E y2 E x2 ) q 3 (E y2 E x2 ) e 1 (E y2 E x2 )

26 Magnetoelectric SHG Source term S ED (P) S MD,EQ ( ) S ED (P ) Sublattice sym. 6mm 6/mmm 6mm SHG for k z = SHG for k x = SH intensity χ yyy k z SH energy (ev) χ zyy χ yyz χ zzz χ yyy k x SH energy (ev) 1 Identical magnetic spectra for k z and k x indicate bilinear coupling to P,. Unarbitrary evidence for the observation of "magnetoelectric SHG"

27 What about domains? Ferroelectric domains Ferroelectric and ferroelectromagnetic SHG contribution allow three experiments: + Ferroelectric domains + + Ferroelectromagnetic domains + + Ferroelectromagnetic domains Antiferromagnetic domains + Antiferromagnetic domains

28 Ferroelectromagnetic Domains Ferroelectric domains Ferroelectric domains + Model,5 mm Ferroelectromagnetic domains + Ferroelectromagnetic domains + Antiferromagnetic domains + Experiment Antiferromagnetic domains

29 Clamping of Antiferromagnetic Domains Coexisting domains in YMnO 3 : clamped Ferroelectric domains: Antiferromagnetic domains: "Magnetoelectric" domains: P = +1 for P = ±1, = ±1 P = -1 for P = ±1, = 1 P P free Any reversal of FEL order parameter clamped to reversal of the AFM order.5 mm FEL FEL & AFM AFM parameter local ME effect Coexistence of "free" and "clamped" AFM walls

30 E-Field induced ME effect Applying an electric field (= ferroelectric poling) above the magnetic phase transition temperature leads to quenching of the magnetic SHG signal! Magnetic SHG image + SH-Intensity (a.u.) 4 χ xxx χ yyy χ xxx χ yyy unpoled poled unpoled poled Transition from α to β order? Temperature (K)

31 Magnetic Phase Control by Electric Field 6mm 6mm Nature 43, 541 (24)

32 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!

33 Summary Nonlinear optics on multiferroics: Nonlinear optics is based on symmetry: χ ijk symmetry structure Simultaneous study of all ferroic structures with the same technique Access to: Electric-magnetic phase diagrams Magnetoelectric interactions Multiferroic domain topology Ultrafast dynamics Etc. etc.

34 Acknowledgements Bonn: Manfred Fiebig Dennis Meier Tim Hoffmann Anne Zimmermann Michael Maringer Tobias Kordel Christian Wehrenfennig Cologne: Ladislav Bohatý Petra Becker Dortmund: Dietmar Fröhlich Stefan Leute Martin Kneip Carsten Degenhard Senta Kallenbach Thorsten Kiefer Matthias Maat Claudia Reimpell Russia: Roman Pisarev Victor Pavlov Japan: Kai Kohn