1. Second harmonic generation on multiferroics Optical spectroscopy seminar 2013 spring Orbán Ágnes, Szaller Dávid 2013. 04. 04.

2. Outline Introduction to nonlinear optics Theoretical background – selection rules The basic idea of the instrumental setup The structure of multiferroic materials Examples: Cr2O3 – domain structure, spin orientation in spin flop phase Hexagonal manganites – spin orientation YMnO3 – multiferro domains

3. Introduction to nonlinear optics Goal: determination/analysis of magnetic and/or electric ordering in crystal strucutres Ususal method: x-ray, electron, neutron diffraction → microscopic structure Nonlinear optics: spatial resolution: 1- 100 µm → visible domain structure surface sensitivity symmetry considerations → resolution of structural ambiguities temporal resolution: 1-10 fs → spin dynamics faster, cheaper How fast?

4. Introduction to nonlinear optics Hamiltonina for light-matter interaction, linear terms: Induced polarozation: For strong EM fields The Kubo-formula:

5. Types of ferro orderings P -q +q -P +q -q r → -r M j -M -j t → -t spontaneous symmetry-breaking multiferroic: ferroic order of more than one degree of freedom extended definition: materials having multiferroic sublattices  includes antiferromagnetic and ferrimagnetic order inversion time reversal

6. Basic symmetry arguments

10. Introduction to nonlinear optics Transformation properties of magnetic crystals: 32 crystallographic pont groups time-reversal operation (T) → 122 magnetic point groups Nonmagnetic crystals: reciprocal susceptibilities, magnetic crystals: additional, nonreciprocal susceptibilities, linear dependence on the relevant order parameter, vanishes above T c, Total SH intensity: Interference term: linear dependence on χ(c) → magnetic order parameter For fixed polarizations χ(i) constant, χ(c) depends on the domain structure

11. Hexagonal manganites RMnO 3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering P6 3 cm in the ferroelectric paramagnetic phase M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)

12. Hexagonal manganites RMnO 3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering P6 3 cm in the ferroelectric paramagnetic phase M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)Phys. Rev. Lett. 84, 5620 (2000)

13. Hexagonal manganites RMnO 3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering P6 3 cm in the ferroelectric paramagnetic phase M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)Phys. Rev. Lett. 84, 5620 (2000)

14. Cr 2 O 3 : magnetic spectroscopy and domain topography Crystal and magnetic structure: Cr 3+ in distorted octahedral errengement of O 2-, chains along the z axis AF magnetic order order parameter: L vector above TN: centrosym. point group 3̅m below TN: 3̅m experiment: k ǁ z →

15. Cr 2 O 3 : magnetic spectroscopy and domain topography cirkuláris bázisban: E = E + e + + E - e - + E z e z, where e ± =± (-1)* (1/√2)(e x ±ie y ) incoming left cirkularly pol. light → right circularly pol. SH incoming right cirkularly pol. light → left circularly pol. SH

16. Cr 2 O 3 : magnetic spectroscopy and domain topography, where C is constant and the second term is the interference change of interference term: reversing the circular polarization or AFM vector same spectra, but with reversed dependence of σ T = 295 K (<T N ), exposure time 35 min, σ + polarized light T = 295 K (<T N ), exposure time 35 min, σ - polarized light T = 325 K (>T N ), exposure time 15 min, σ +/- polarized light

17. Cr 2 O 3 : spin-flop phase Crystal and magnetic structure: Cr 3+ in distorted octahedral errengement of O 2-, chains along the z axis AF magnetic order order parameter: L vector above T N : centrosym. point group 3̅m below T N : 3̅m spin-flop phase: below T N, B=5.8 T ǁ z, AFM order 3-fold rotation is lost, six possible domains two possibilities: Lǁy, where y is the twofold axis, 2/m Lǁx, where x is the glid plane, 2/m experiment: E y polarization

18. Magnetic dipole SHG M. Fiebig, et. al. PRL, 87 137202 (2001)