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

1 Θ ...3i i ij i j B i iδH ε p E ε E μ m B

1 Θ0 00 0 0

1Δ ...3

ω ω m ωij j ijk j k B ij jω

P 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 3̅m

• below TN: 3̅m

• 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 3̅m • below TN: 3̅m• 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)