1. Magneto-optical imaging of Superconductors Satyajit S.Banerjee Dept of Physics, Indian Institute of Technology, Kanpur, India

2. Principle of operation of MO imaging Faraday Effect: P A Light source Polariser d M M M Analyser Z Y X Z P A  F = V B z d Transmission Mode

3. Reflection Mode MO Polarized light GGG M Sample  F = V B z 2d d Protective layer Reflecting layer MO active layer Z YX

4. Types of MO active layers Type of MO active layer depends on the type of experiments. YIG EuSe EuTe d

5. 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=I o Sin 2 (2VdB z ) or I  B z 2

6. 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 Sample z

7. 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

8. Some basic ideas about vortices a 0 ~(  0 /B) 1/2 At B = 1 T, a 0 ~500 A 0  ~ 5 x 10 10 vortices/cm 2 2  ~5-10 nm

9. Loss of sensitivity in resolving vortices with increasing dist. With increasing distance of the MO active layer from the surface of the superconductor causes loss of the resolving power for resolving vortices.

10. Applications of MO at Mesoscopic length scales Observing the Meissner effect in superconductors Observing the Critical state YBCO, 10 K, field of 10 G YBCO, 70 K, field of 100mT Strong meissner screening currents on surface B x 0

11. Phase transitions in the vortex state Similarities between ice to water transition & Vortex solid to liquid transition 213.3 213.4 58.3558.4058.4558.5058.55 T [ K ] H a = 240 Oe liquid solid  B~0.2G  B~0.1%B B(G)  vor  B solid kBTkBT ordered liquid disordered

12. 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

13. 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=10 4 Photon shot noise N/  N = (N) 1/2  N=10 8 photons/pixel CCD full well capacity ~10 5 electrons  ~10 3 frames Reduce static noise by differential process: …~100 times n~10 n down HaHa Ha+HaHa+Ha n up differential static noise   H a static noise  H a

14. Observation of melting in MOI  P A image light source mirror MO indicator S N large small FF F=BF=B temperature scan 213.0 213.1 213.2 213.3 213.4 58.3558.4058.4558.5058.55 T [ K ] H a = 240 Oe liquid solid  B~0.2G  B~0.1%B B(G) Difference image: Solid (no change in B) Liquid change in B already occurred Dept. of Condensed Matter Physics Weizmann Institute Of Science

15. Movie of melting in a HTSC superconductor

16. Phase diagram of melting 10 1 10 2 10 3 10 4 10 5 020406080100 first-order transition second magnetization peak H c2 T [ K ] B [ G ] depinning disordered quasi-ordered-lattice (Bragg glass) liquid solid

17. Effect of disorder on melting Sample Bi 2 Sr 2 CaCu 2 O 8 (BSCCO), T c ~ 89-90 K SST mask 90  m Columnar defects

19. Melting phase diagram in presence of disorder Porous vortex solid Vortex Liquid ? S. S. Banerjee et al, Phys. Rev. Lett. 90, 87004 (2003)

20. Imaging transport current distribution using MOI (MO Image with I+) - (MO Image with I-) = Difference Image Fixed H,T Sample with uniform I distribution Self field generated by I (Biot-Savarts law) Schematic of self field image one should see Inversion scheme Wijngaarden et al PRB54, 6742 (96) Can detect self field down to 0.1 mA Two to three orders of magnitude improvement in sensitivity S. S. Banerjee et al, Phys. Rev. Lett. 93, 97002 (2004)

21. Some examples :Surface barrier BSCCO crystal 0.5 mm Current distribution Self-induced field 30mA, 75K, 25G - I- I- I- I + I - V- V- V- V + V

22. Imaging current distribution in the vortex liquid phase Irradiated Unirradiated NL S. S. Banerjee et al, Phys. Rev. Lett. 93, 97002 (2004)

23. Micron-submicron resolution Single vortex imaging with MO GGG M Sample d Reflecting layer Protective layer Conventional MO indicator: Latest MO indicator: GGG M Sample MO layer Prof. Tom Johansens Group, Oslo, Norway

24. Dynamics of single vortices Interaction of magnetic Domain walls with vortices

25. Nanosecond temporal resolution Paul Leidere ’ s group, University of Konstadz, Germany

26. 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

27. 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.

28. Acknowledgements Prof Eli Zeldov, Israel Prof Yossi Yeshurun, Israel. Prof. Marcin Konczykowski,France Prof. Kees van der Beek, France Prof. Tsuyoshi Tamegai, Japan Prof. M. Indenbom, Russia Prof Tom Johansen, Oslo Prof. Paul Leiderer, Germany Prof. A. A. Polyanski, USA Prof. Vlasko Vlasov, USA Prof. U. Welp, USA Prof. Larbalestier, USA Prof. H. Brandt