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ISOM2000 Tutorial
Introduction to Magneto-Optics
Katsuaki SatoDepartment of Applied Physics
Tokyo University of Agriculture & Technology
CONTENTS
1. Introduction2. Light and Magnetism3. What is the Magneto-Optical Effect?4. Electromagnetism and Magneto-Optics5. Electronic Theory6. Measurement of Magneto-Optical Effect7. Magneto-Optical Spectra 8. Recent Advances in Magneto-Optics9. Summary
1. Introduction
• Magneto-Optical Effect: Discovered by Faraday on 1845
• Phenomenon: Change of Linear Polarization to Elliptically Polarized Light Accompanied by Rotation of Principal Axis
• Cause: Difference of Optical Response between LCP and RCP
• Application:– Magneto-Optical Disk
– Optical Isolator
– Current Sensors
– Observation Technique
2. Light and Magnetism
• Light→Magnetism : Photomagentic Effect– Thermomagnetic Effect : Curie pt. recording→MO disk– Light-induced Magnetization : ruby, DMS– Light-induced spin reorientation→Optical motor
• Magnetism→Light : Magneto-Optical Effect– Shift or splitting of optical absorption line(Zeeman eff.)– Magnetic resonance : ESR, magneto-plasma effect– Magneto-optical effect(Faraday, Kerr, Cotton Mouton)
3.What is the Magneto-Optical Effect?
• MO Effect in Wide MeaningAny change of optical response induced by magnetizatio
n
• MO Effect in Narrow MeaningChange of intensity or polarization induced by magentizat
ion – Faraday effect– MOKE(Magneto-optical Kerr effect)– Cotton-Mouton effect
3.1 Faraday & Voigt Configurations
• (a) Faraday Configuration: – Magnetization // Light Vector
• (b)Voigt Configuration:– Magnetization Light Vector
3.2 Faraday Effect• MO effect for optical transmission
– Magnetic rotation ( Faraday rotation ) F
– Magnetic Circular Dichroism ( Faraday Ellipticity ) F
• Comparison to Natural Optical Rotation– Faraday Effect is Nonreciprocal (Double rotation for round tr
ip)
– Natural rotation is Reciprocal (Zero for round trip)
• Verdet Constant F=VlH (For paramagnetic and diamagnetic materials )
Illustration of Faraday Effect
For linearly polarized light incidence,
• Elliptically polarized light goes out (MCD)
• With the principal axis rotated (Magnetic rotation)
Linearly polarized light
EllipticallyPolarized light
Rotation of Principal axis
3.3 Faraday rotation of magnetic materialsMaterials rotation
(deg) figure of
merit(deg/dB)wavelength
(nm)temperat
ure(K)
Mag. field(T)
literature
Fe 3.825 ・ 105 578 RT 2.4 1.11)
Co 1.88 ・ 105 546 〃 2 1.11)
Ni 1.3 ・ 105 826 120 K 0.27 1.11)
Y3Fe5O12 250 1150 100 K 1.12)
Gd2BiFe5O12 1.01 ・ 104 44 800 RT 1.13)
MnSb 2.8 ・ 105 500 〃 1.14)
MnBi 5.0 ・ 105 1.43 633 〃 1.15)
YFeO3 4.9 ・ 103 633 〃 1.16)
NdFeO3 4.72 ・ 104 633 〃 1.17)
CrBr3 1.3 ・ 105 500 1.5K 1.18)
EuO 5 ・ 105 104 660 4.2 K 2.08 1.19)
CdCr2S4 3.8 ・ 103 35(80K) 1000 4K 0.6 1.20)
3.4 Magneto-Optical Kerr Effect
• Three kinds of MO Kerr effects– Polar Kerr ( Magnetization is oriented perpen
dicular to the suraface )– Longitudinal Kerr ( Magnetization is in plane
and is parallel to the plane of incidence )– Transverse Kerr ( Magnetization is in plane
and is perpendicular to the plane of incidence )
3.5 MO Kerr rotation of magnetic materialsaterials rotation Photon
energytemperat
urefield literature
(deg) (eV) (K) (T)
Fe 0.87 0.75 RT 1.21)
Co 0.85 0.62 〃 1.21)
Ni 0.19 3.1 〃 1.21)
Gd 0.16 4.3 〃 1.22)
Fe3O4 0.32 1 〃 1.23)
MnBi 0.7 1.9 〃 1.24)
PtMnSb 2.0 1.75 〃 1.7 1.8)
CoS2 1.1 0.8 4.2 0.4 1.25)
CrBr3 3.5 2.9 4.2 1.26)
EuO 6 2.1 12 1.27)
USb0.8Te0
.2
9.0 0.8 10 4.0 1.28)
CoCr2S4 4.5 0.7 80 1.29)
a-GdCo *
0.3 1.9 RT 1.30)
CeSb 90 2 1.31)
4. Electromagnetism and Magnetooptics
• Light is the electromagnetic wave.• Transmission of EM wave : Maxwell equation• Medium is regareded as continuum→dielectric permeabi
lity tensor– Effect of Magnetic field→mainly to off-diagonal element
• Eigenequation• →Complex refractive index : two eigenvalues
eigenfunctions : right and left circularpolarization– Phase difference between RCP and LCP→rotation– Amplitude difference →circular dichroism
4.1 Dielectric tensor
ED 0~ ε
zzzyzx
yzyyyx
xzxyxx~
ijijij
Isotromic media ; M//zInvariant C4 for 90°rotation around z-axis
zzzxzy
xzxxxy
yzyxyy
CC 41
4~~
0
zyzxyzxz
xyyx
yyxx
zz
xxxy
xyxx
00
0
0~
4.2 MO Equations (1)
0~
2
2
2
Etc
Erotrot
0
00
0ˆ0ˆ
2
2
z
y
x
zz
xxxy
xyxx
E
E
E
N
N
xyxx iN 2ˆEigenvalue
Eigenfunction : LCP and RCP
Without off-diagonal terms: No difference between LCP & RCP
No magnetooptical effect
Maxwell Equation
Eigenequation
MO Equations (2)
xx
yxyxxxyxxx iiiNNN
ˆˆˆ
2)2(21)0(
)1(
ˆ
M
Mi
iN
xxxx
xy
xx
yxF
Both diagonal and off-diagonal terms contribute toMagneto-optical effect
4.3 Phenomenology of MO effectLinearly polarized light can be decomposed to LCP and RCP
Difference in phase causes rotation ofthe direction of Linear polarization
Difference in amplitudes makes Elliptically polarized light
In general, elliptically polarized lightWith the principal axis rotated
5. Electron theory of Magneto-Optics
• Magnetization→Splitting of spin-states– No direct cause of difference of optical response
between LCP and RCP
• Spin-orbit interaction→Splitting of orbital states– Absorption of circular polarization→Induction of circular
motion of electrons
• Condition for large magneto-optical response– Presence of strong (allowed) transitions– Involving elements with large spin-orbit interaction– Not directly related with Magnetization
5.1 Microscopic concepts of electronic polarization
= +++ + ・・
+ + -
-
Unperturbed wavefunction
Wavefunction perturbed by electric field
E
S-like P-like
Expansion by unperturbed orbitals
5.2 Orbital angular momentum-selection rules and circular dichroism
Lz=0
Lz=+1
Lz=-1
s-like
p-=px-ipy
p+=px+ipy
px-orbitalpy-orbital
5.3 Role of Spin-Orbit Interaction
L=1
L=0
LZ=+1,0,-1
LZ=0
Jz=-3/2Jz=-1/2
Jz=+1/2Jz=+3/2
Jz=-1/2
Jz=+1/2
Exchange splitting
Exchange
+spin-orbit
Without magnetization
5.4 MO lineshapes (1)
Excited state
Ground state
0 1 2
Without magnetization
With magnetization
Lz=0
Lz=+1
Lz=-1
1+2
Photon energy Photon energy
’xy ”xy
1.Diamagnetic lineshape
5.4 MO lineshapes (2)
excited state
ground state
f+ f-
f=f+ - f-
0
without magneticfield
with magneticfield
’xy
”xy
photon energy
(a) (b)d
iele
ctri
c co
nst
ant
6. Measurement of MO effect
1. Cross-polarizer technique
2. Vibrating polarizer technique
3. Rotating analyzer technique
4. Faraday modulation technique
5. Optical retardation modulation
6. Measuring system for MO spectrum
7. Measurement of elleipticity
L
P B A
D
PF A I
P=A+/2
/4 rotation
/2 rotation
rotation
B
(a)
(b)
S
6.1 Cross-Nicol technique
P
B
P
F
+F
AD
ID
S
6.2 Vibrating polarizer technique
PA
DS
BEF
A=pt
ID
6.3 Rotating analyzer technique
Faraday modulator
P
=0+sin pt
B
S
A
DI=I0+ I sin pt
F ID
6.4 Faraday modulation technique
Zero method
i
j
/4
P
PEM A
D
quartz Isotropicmedium
B
fused silica CaF2
Ge etc.
Piezoelectriccrystal
amplitude
position
l
Retardation=(2/)nl sin pt =0sin pt
6.5 Retardation modulation technique
L MC
P
AC (f Hz)
M1
M2
PEM(p Hz) S
Electromagnet
D
Preamplifier
LA1 (f Hz)
LA2 (p Hz)
LA3 (2p Hz)
6.6 Spectral measurement
x
y
x’y’
/4plate
E0
E0sin
E0cos
E E i i j 0 (cos sin )
Opticaxis
E E i i e j
E i j
E i
i' (cos sin )
cos sin
'
02
0
0
x
y
E’
E
6.7 Measurement of ellipticity
7. MO spectra of materials
• Magnetic garnets• Metallic ferromagnet : Fe, Co, Ni• Intermetallic compounds and alloys : PtMnSb et
c.• Magnetic semiconductor : CdMnTe etc.• Superlattices : Pt/Co, Fe/Au etc.• Amorphous : TbFeCo, GdFeCo etc.• Granular : Al2O3:Co など
Theory and experiment of MO spectra in Fe
Katayama
theory
(a) (b) (c)
MO spectra of PtMnSb
カー回転と楕円率 誘電率対角成分 誘電率非対角成分
xxxx
xyK
1
Wavelength (nm)P
ola
r K
err
ro
tatio
n (
min
)
MO spectra in RE-TM (1)
5 4 3 2
Photon Energy (eV)
0
-0.2
-0.4
-0.6
Pol
ar
Ker
r ro
tatio
n (d
eg)
Wavelength (nm)
300 400 500 600 700
MO spectra in RE-TM(2)
Recent Advances in Magneto-Optics
• Scanning Near Field Magneto-Optical Microscope (MO-SNOM)
• Nonlinear Magneto-Optics
• Sagnac Magneto-Optical Microscope
• X-ray Magneto-Optical Imaging
SUMMARY
• Basic concept of magneto-optics is described.
• Macroscopic and microscopic origins of magneto-optics are described.
• Some of the recent development of magneto-optics is also given.