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Transcript of Second harmonic generation on multiferroics Optical spectroscopy seminar 2013 spring Orbán Ágnes,...
Second harmonic generation on multiferroicsOptical 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
• The structure of multiferroic materials
• Examples:
• Cr2O3 – domain structure, spin orientation in spin flop phase
• Hexagonal manganites – spin orientation
• YMnO3 – multiferro domains
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?
Introduction to nonlinear optics
• Hamiltonina for light-matter interaction, linear terms:
• Induced polarozation:
• For strong EM fields
• The Kubo-formula:
00 00 0
1Θ ...
3i i ij i j B i iδH ε p E ε E μ m B
1 Θ0 00 0 0
1Δ ...
3ω ω m ω
ij j ijk j k B ij jωP ε χ E ε χ E μ χ B
2 ω ω0 ijk j kε χ E E1 3
0 0Δ ...ω ω ω ωij j ijkm j k mP ε χ E ε χ E E E
Types of ferro orderings
P-q
+q-P
+q
-q
r → -r
M
j
-M
-jt → -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
inversiontime
reversal
Basic symmetry arguments
• Paramagnetic or nonmagnetic, centro-symmetric material– Spatial inversion and time reversal symmetry,
• Paramagnetic or nonmagnetic, centro-symmetric material– Spatial inversion and time reversal symmetry,
𝜒𝑒𝑒𝑒=0
𝑀 2𝜔 𝜒𝑚𝑒𝑒𝐸𝜔𝐸𝜔
Basic symmetry arguments
• Paramagnetic or nonmagnetic, centro-symmetric material– Spatial inversion and time reversal symmetry,
• Magnetic phase,
𝜒𝑒𝑒𝑒=0
𝜒𝑚𝑒𝑒 (𝑖)𝑀 2𝜔 𝜒𝑚𝑒𝑒𝐸𝜔𝐸𝜔
Basic symmetry arguments
• Paramagnetic or nonmagnetic, centro-symmetric material– Spatial inversion and time reversal symmetry,
• Magnetic phase,
𝜒𝑒𝑒𝑒=0
𝜒𝑚𝑒𝑒 (𝑖)𝑀 2𝜔 𝜒𝑚𝑒𝑒𝐸𝜔𝐸𝜔
𝜒𝑒𝑒𝑒 (𝑐)
Basic symmetry arguments
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 Tc,
• 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
ijkχ i
ijkχ c
Hexagonal manganites
• 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)
𝑃 63𝑐𝑚𝑃 63𝑐𝑚
Hexagonal manganites
• 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)
𝑃 63𝑐𝑚𝑃 63𝑐𝑚
Phys. Rev. Lett. 84, 5620 (2000)
Hexagonal manganites
• 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) Phys. Rev. Lett. 84, 5620 (2000)
Cr2O3 : magnetic spectroscopy and domain topography
• Crystal and magnetic structure:
• Cr3+ in distorted octahedral errengement of O2- , chains along the z axis• AF magnetic order• order parameter: L vector• above TN: centrosym. point group 3Om
• below TN: 3Om
• experiment: k ǁ z → m m m mm yyy yxx xyx xxyχ i χ i χ i χ i χ i
m m m mm yyy yxx xyx xxyχ c χ c χ c χ c χ c
Cr2O3 : magnetic spectroscopy and domain topography
• cirkuláris bázisban: E = E+e+ + E-e- + Ezez, where e±=± (-1)* (1/√2)(ex±iey)
• incoming left cirkularly pol. light → right circularly pol. SH incoming right cirkularly pol. light → left circularly pol. SH
Cr2O3 : 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 (<TN), exposure time 35 min, σ+ polarized light
T = 295 K (<TN), exposure time 35 min, σ- polarized light
T = 325 K (>TN), exposure time 15 min, σ+/- polarized light
Cr2O3 : spin-flop phase
• Crystal and magnetic structure:
• Cr3+ in distorted octahedral errengement of O2- , chains along the z axis• AF magnetic order• order parameter: L vector• above TN: centrosym. point group 3Om • below TN: 3Om• spin-flop phase: below TN, 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: Ey polarization
Magnetic dipole SHG
𝑀 2𝜔 𝜒𝑚𝑒𝑒𝐸𝜔𝐸𝜔
M. Fiebig, et. al. PRL, 87 137202 (2001)