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Magneto-optical imaging of Superconductors
Satyajit S .BanerjeeDept of Physics,
Indian Institute of Technology,Kanpur, India
Principle of operation of MO imaging
• Faraday Effect:
P A
Light source
Polariser
d
MM
M
Analyser
ZY
X
Z
P A
F = V Bz d
Transmission Mode
Reflection Mode MO
Polarized light
GGGM
Sample
F = V Bz 2d
d
Protective layerReflecting layer
MO active layer
Z
Y X
Types of MO active layers
• Type of MO active layer depends on the type of experiments.
10-1-2-31010101010
3
2
1
10
10
10
010
T(K
)
B(T)
YIG
EuSe
EuTe
d
MO imaging setup
Choice YIG : For high magnetic field resolution and
Wide T range of application
Typical Faraday rotation: 0.06 deg/mT for 2-5 m thick indicators I=IoSin2(2VdBz) or
I Bz2
Sensitivity of the MO technique
• Field sensitivity is determined by the Faraday rotation 2Vd & noise
For EuTe~20mT for Bi doped YIG ~ 0.15 mT
• Spatial resolution
Governed by thickness (d) + distance between sample and MO active layer (z)
d
Samplez
Sensitivity of the MO technique
• Temporal resolution
Governed by the Quantum efficiency and the minimum exposure time permissible by the imaging device like a video camera.
Temporal resolution ~ at best a few mSecs
In recent times there have been nearly two to three order of magnitude improvement in field, spatial and temporal resolution
Some basic ideas about vortices
a0~(0/B)1/2
At B = 1 T, a0~500 A0
~ 5 x 1010 vortices/cm2
2~5-10 nm
rforr
rforr
F
exp
ln
Loss of sensitivity in resolving vortices with increasing dist.
With increasing distance of the MO active layer from the surfaceof the superconductor causesloss of the resolving powerfor resolving vortices.
Applications of MO at Mesoscopic length scales
• Observing the Meissner effect in superconductors
•Observing the Critical stateYBCO, 10 K, field of 10 G
YBCO, 70 K, field of 100mT
Strong meissner screening currents on surface
B
x0
)()( rJrB c
Phase transitions in the vortex state
Similarities between ice to water transition & Vortex solid to liquid transition
213.0
213.1
213.2
213.3
213.4
58.35 58.40 58.45 58.50 58.55
T [ K ]
H a = 240 Oe
liquid
solid
B~0.2GB~0.1%BB
(G) vor B
solid
kBT
ordered
liquid
disordered
Source of noise in MOI
Dynamic:
• CCD noise• Light fluctuations• Vibrations
Fundamental noise:
• Photon shot noise
Static:
• Indicator inhomogeneities and defects• CCD pixel variations • Light inhomogeneities
B(x) » 1 G
Differential MOI imaging
dc field B = 100 G
• Equilibrium magnetization step B 0.1 G • Desired resolution ~0.01 G• Required signal/noise 100/0.01=104
• Photon shot noise N/N = (N)1/2 N=108 photons/pixel• CCD full well capacity ~105 electrons ~103 frames• Reduce static noise by differential process:
…~100 timesn~10 n downHa
Ha+Ha
n upn up
0.0
2000.0
4000.0
6000.0
8000.0
10000.0
0 100 200 300 400 500 600 700 800
0 100 200 300 400 500 600 700 800
differential static noise Ha
static noise Ha
Observation of melting in MOI
P
A
image
light source
mirrorMO indicator
SN
largesmall small
FF=
B
temperature scan
213.0
213.1
213.2
213.3
213.4
58.35 58.40 58.45 58.50 58.55
T [ K ]
H a = 240 Oe
liquid
solidB~0.2G
B~0.1%BB(G
)
Difference image:
Solid(no change in B)
Liquidchange in B already occurred
Dept. of CondensedMatter Physics Weizmann Institute Of Science
Phase diagram of melting
101
102
103
104
105
0 20 40 60 80 100
first-ordertransition
secondmagnetization
peak
Hc2
T [ K ]
B
[ G ]
depinningdisordered
quasi-ordered-lattice(Bragg glass)
liquid
solid
Effect of disorder on meltingSample Bi2Sr2CaCu2O8 (BSCCO), Tc ~ 89-90 K
SST maskSST mask 9090 mmColumnar defects
50 60 70 80 900
50
100
150
200 Melting withdisorder
Melting withoutdisorder
T(K)
B(G
)
Melting phase diagram in presence of disorder
Porous vortex solid
VortexLiquid ?
S. S. Banerjee et al, Phys. Rev. Lett. 90, 87004 (2003)
Imaging transport current distribution using MOI
(MO Image with I+) - (MO Image with I-) = Difference Image FixedH,T
Sample with uniform I distribution
Self field generated by I(Biot-Savarts law)
Schematic of self fieldimage one should see
InversionschemeWijngaardenet alPRB54,6742 (96)
Can detect self field down to 0.1 mATwo to three orders of magnitude improvement in sensitivity
S. S. Banerjee et al, Phys. Rev. Lett. 93, 97002 (2004)
Some examples :Surface barrier
BSCCO crystalBSCCO crystal
0.5 mm
Current distributionCurrent distributionSelf-induced fieldSelf-induced field
30mA, 75K, 25G 30mA, 75K, 25G
-- I I
+ I+ I
-- V V
+ V+ V
Imaging current distribution in the vortex liquid phase
Irradiated
Unirradiated
NL
50 60 70 80 900
50
100
150
200
0Bm
CDBm
homogeneous liquid
nanoliquid
B = 60 G
B (G
)
T (K)
Bdl
S. S. Banerjee et al, Phys. Rev. Lett. 93, 97002 (2004)
Micron-submicron resolution
• Single vortex imaging with MO
GGG M
Sample
d
Reflecting layerProtective layer
Conventional MO indicator:
Latest MO indicator:
GGG M
Sample
MO layer
Prof. Tom Johansens Group,Oslo, Norway
Dynamics of single vortices
Interaction of magneticDomain walls with
vortices
Nanosecond temporal resolution
Paul Leidere’s group, University of Konstadz, Germany
Application of MO in different areas of condensed matter physics
Dilute magnetic semiconductors (Mn doped GaAs)U. Welp et al., PRL 90, 167206 (2003)
L.E.Helseth et al,PRL 91, 208302 (2003)
Manipulating magnetic beads
Summary
• Two orders of magnitude improvements in spatial, temporal and magnetic field sensitivity.
• Improvement in transport current detection capability
• Enormous potential for investing the physics of magnetic response in a diverse class of materials.
Acknowledgements
Prof Eli Zeldov, IsraelProf Yossi Yeshurun, Israel.
Prof. Marcin Konczykowski,FranceProf. Kees van der Beek, FranceProf. Tsuyoshi Tamegai, Japan
Prof. M. Indenbom, RussiaProf Tom Johansen, Oslo
Prof. Paul Leiderer, GermanyProf. A. A. Polyanski, USAProf. Vlasko Vlasov, USA
Prof. U. Welp, USAProf. Larbalestier, USA
Prof. H. Brandt