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Second harmonic generation on multiferroics

Second harmonic generation on multiferroics. Optical spectroscopy seminar 2013 spring Orbán Ágnes, Szaller Dávid 2013. 04. 04. Outline. Introduction to nonlinear optics Theoretical background – selection rules The basic idea of the instrumental setup

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Second harmonic generation on multiferroics

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  1. Secondharmonicgenerationonmultiferroics Opticalspectroscopyseminar 2013 spring Orbán Ágnes, Szaller Dávid2013. 04. 04.

  2. Outline • Introductiontononlinearoptics • Theoreticalbackground – selectionrules • The basic idea of theinstrumentalsetup • The structure of multiferroicmaterials • Examples: • Cr2O3 – domainstructure, spin orientationinspinflopphase • Hexagonalmanganites – spin orientation • YMnO3 – multiferrodomains

  3. Introductiontononlinearoptics • Goal: determination/analysis of magnetic and/orelectricorderingincrystalstrucutres • Ususalmethod: x-ray, electron, neutron diffraction → microscopicstructure • Nonlinearoptics: • spatialresolution: 1- 100 µm → visibledomainstructure • surfacesensitivity • symmetryconsiderations → resolution of structuralambiguities • temporalresolution: 1-10 fs → spin dynamics • faster, cheaper Howfast?

  4. Introductiontononlinearoptics • Hamiltoninaforlight-matterinteraction, linearterms: • Inducedpolarozation: • Forstrong EM fields • The Kubo-formula:

  5. Types of ferroorderings M -M +q -q P -P time reversal j -j -q +q inversion r → -r t → -t • spontaneoussymmetry-breaking • multiferroic: ferroicorder of more thanonedegree of freedom • extendeddefinition: materialshavingmultiferroicsublattices •  includesantiferromagnetic and ferrimagneticorder

  6. Basic symmetryarguments • Paramagnetic ornonmagnetic, centro-symmetricmaterial • Spatialinversion and timereversalsymmetry,

  7. Basic symmetryarguments • Paramagnetic ornonmagnetic, centro-symmetricmaterial • Spatialinversion and timereversalsymmetry,

  8. Basic symmetryarguments • Paramagnetic ornonmagnetic, centro-symmetricmaterial • Spatialinversion and timereversalsymmetry, • Magnetic phase,

  9. Basic symmetryarguments • Paramagnetic ornonmagnetic, centro-symmetricmaterial • Spatialinversion and timereversalsymmetry, • Magnetic phase,

  10. Introductiontononlinearoptics • Transformationproperties of magneticcrystals: • 32 crystallographic pont groupstime-reversaloperation (T) → 122 magneticpointgroups • Nonmagneticcrystals: reciprocalsusceptibilities, • magneticcrystals: additional, nonreciprocalsusceptibilities, lineardependenceontherelevantorderparameter, vanishesaboveTc, • Total SH intensity: • Interferenceterm: lineardependenceonχ(c) → magneticorderparameter • For fixed polarizationsχ(i) constant, χ(c) dependsonthedomainstructure

  11. Hexagonalmanganites • RMnO3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu • simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering • P63cm in the ferroelectric paramagnetic phase M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)

  12. Hexagonalmanganites • RMnO3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu • simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering • P63cm in the ferroelectric paramagnetic phase Phys. Rev. Lett. 84, 5620 (2000) M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)

  13. Hexagonalmanganites • RMnO3 with R=Sc, Y, In, Ho, Er, Tm, Yb, Lu • simultaneous ferroelectric and frustrated triangular antiferromagnetic ordering • P63cm in the ferroelectric paramagnetic phase Phys. Rev. Lett. 84, 5620 (2000) M. Fiebig, R.V. Pisarev, JMMM, 272 e1607 (2004)

  14. Cr2O3 : magneticspectroscopy and domaintopography • Crystal and magneticstructure: • Cr3+indistortedoctahedralerrengement of O2- , chainsalongthezaxis • AF magneticorder • orderparameter: L vector • above TN: centrosym. pointgroup 3̅m • below TN: 3̅m • experiment: k ǁ z →

  15. Cr2O3 : magneticspectroscopy and domaintopography • cirkuláris bázisban: E = E+e+ + E-e- + Ezez, wheree±=± (-1)* (1/√2)(ex±iey) • incomingleftcirkularlypol. light → right circularlypol. SH • incoming right cirkularlypol. light → leftcircularlypol. SH

  16. Cr2O3 : magneticspectroscopy and domaintopography • , where C is constant and thesecondterm is theinterference • change of interferenceterm: reversingthecircularpolarizationorAFM vector • samespectra, butwithreverseddependence of σ T = 295 K (<TN), exposuretime 35 min, σ+polarizedlight T = 295 K (<TN), exposuretime 35 min, σ-polarizedlight T = 325 K (>TN), exposuretime 15 min, σ+/-polarizedlight

  17. Cr3+indistortedoctahedralerrengement of O2- , chainsalongthezaxis • AF magneticorder • orderparameter: L vector • above TN: centrosym. pointgroup 3̅m • below TN: 3̅m • spin-flopphase: below TN, B=5.8 T ǁ z, AFM order • 3-fold rotation is lost, sixpossibledomains • twopossibilities: • Lǁy, wherey is thetwofoldaxis, 2/m • Lǁx, wherex is theglidplane, 2/m • experiment: Eypolarization Cr2O3 : spin-flopphase • Crystal and magneticstructure:

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

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