Magneto-Optical Imaging of Superconductors

 

Contents of this page: Fundamentals of magneto-optical imaging Basic Properties of Superconductors Variety of superconducting materials Quality control: observation of defects Phenomena in Superconductors Advanced methods

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Fundamentals of magneto-optical imaging

 

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Physical principles The physical idea behind the magneto-optical imaging is the Faraday effect, i.e., rotation of the light polarization induced by magnetic field. On 13 September, 1845, Michael Faraday wrote in his Diary "...magnetic force and light were proved to have relation to each other. This fact will most likely prove exceedingly fertile and of great value in the investigation of both conditions of natural force" .

 

 

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Magneto-optical films A number of different materials have been applied as indicators in MO imaging: cerous nitrate-glycerol, various europium compounds (EuS, EuSe) [H. Kirchner, Phys. Lett. 26A, 651 (1968)] and bismuth-substituted iron garnets [A.A. Polyanskii et al. Sov. Tech. Phys. Lett. 15, 872 (1989)]. Today, the most popular indicator is the ferri-magnetic Bi:YIG film with in-plane spontaneous magnetization. Application of a perpendicular magnetic field creates an out-of-plane component of the magnetization responsible for the Faraday rotation. A single-crystal film with typical thickness of a few microns can be grown by liquid-phase epitaxy on a gadolinium-gallium-garnet (GGG) substrate.

 

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Rotation angle vs. magnetic field dependence At small magnetic fields the polarization rotation angle depends on the field linearly, angle=d V H, where d is the distance travelled by the light in the medium, and V is a material parameter called the Verdet constant. Typically, V is of the order of 0.1 degree/mT micron. At sufficiently high fields the indicator saturates as its magnetization vector becomes maximally aligned with the field.

 

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Magneto-optical setup The MO indicator is placed in the light beam path between a polarizer and an analyzer crossed by 90 degrees. If a magnetic field is present perpendicularly to the film, the magnetization of the Bi:YIG will be tilted out of the plane. The perpendicular component of the magnetization will cause a Faraday rotation of the light. The rotation angle will be small where the magnetic field is small, and large in regions of high fields. After leaving the analyzer the light will therefore have an intensity distribution that reflects the magnitude of the field in the plane of the indicator film.

 

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Basic Properties of Superconductors

 

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Meissner effect When a superconductor is cooled down below the critical temperature, Tc, its resistance to electrical current is known to disappear. The other fundamental property of superconductors is so-called Meissner effect, i.e., expulsion of magnetic field. An external field is entirely compensated by shielding currents which it induces in the superconductor, and which will flow forever due to absence of resistance.

 

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Observation of the Meissner effect A square superconducting film was cooled below the critical temperature in zero magnetic field. Then a small perpendicular field was applied. The MO image shows that the field does not penetrate the superconductor (black corresponds to zero field). The magnetic field lines have to bend around the superconductor, and thus concentrate near the edges which are the brightest areas on the image.

 

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Critical state in type-II superconductors When the external field exceeds the first critical field Hc1, the magnetic flux can penetrate type-II superconductor in form of Abrikosov vortices (flux lines), each carrying one quantum of magnetic flux, h/2e. The flux penetration is hindered by microscopic inhomogeneities which pin (trap) vortices. As a result, a critical state is formed with some gradient of flux density determined by the critical current.

 

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Observation of the critical state The MO image shows flux penetration in a zero-field-cooled film placed in a perpendicular magnetic field. Similar to the Meissner state, the brightest areas are found at the edges where the expelled flux concentrates. At the same time, the flux already penetrated deep inside the superconductor from the sides of the square. Only the corners and the central part remain flux free (completely black).

 

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Trapped flux in the remanent state After applying a large magnetic field which is subsequently decreased down to zero, a large amount of magnetic flux remains trapped in the superconductor, see the MO image. The maximum flux density is found in the center and along the diagonals.   The magnetic lines close up near the edges, and the bright regions seen there correspond to the return flux, i.e. magnetic field in the opposite direction. Between the central peak and the edge lies black annihilation zone, free of magnetic flux (the image brightness represents the absolute value of the flux density).

 

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large maximum field: AVI movie (DivX coding) 140Kb MPEG movie 270Kb QuickTime movie 330Kb small maximum field: AVI movie 140Kb MPEG movie 350Kb

Full cycle: increasing and decreasing field A zero-field-cooled superconducting film was placed in a magnetic field first increasing to a very high value and then decreasing back to zero. A movie was combined from a series of MO images taken during this process. As the field increases, one can see smooth advancement of the flux front from the sides, until only two diagonals remain free of flux. During the field descent, on contrary, the diagonals represent the regions of maximum flux density, while the minimum is found at the edges (dark). Finally, when the field decreases back to zero, the edges become bright again indicating the return flux as on the previous image. In the case of a small maximum field, the flux penetration is not complete, and the center with two diagonals always remain flux-free.

 

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Flux penetration in a triangular film The magnetic flux distribution in a superconductor is strongly dependent on its shape. Here are MO images of the Meissner state, partial penetration and the remanent state for a triangular YBaCuO film at 4.2K Image: Jooss et al., Rep. Prog. Phys. 65, 651 (2002).

 

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Variety of superconducting materials

You can not really tell what is going on inside a superconductor if only integral characteristics (like magnetization or resistance) are measured. You do need to see magnetic behavior with your own eyes because every superconducting sample has its unique magneto-optical image.

 

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Melt-Powder-Melt-Growth NdBa2Cu3O7

Hg-based ceramic

 

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Granular YBa2Cu3O7

Nb foil

 

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YBa2Cu3O7 film the right half of the sample was irradiated with heavy high-energy ions

YBa2Cu3O7 coated conductor the field penetrates preferentially along grain boundaries Image: Applied Superconductivity Center

 

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Quality control: observation of defects

Application of magnetic field induces in superconductor screening currents. If there exists a defected region where the current flow is distorted, it is reflected in the magnetic field distribution, which is immediately seen in magneto-optical images.

 

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Single defect in a YBa2Cu3O7 film MO imaging allows easy detection of defected regions in a superconducting sample. A single defect produces a big disturbance of the flux pattern as the applied magnetic field increases.

 

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Slits in a YBa2Cu3O7 film An extended defect perpendicular to the direction of shielding currents can be detected from MO images already at very small applied fields. Interestingly, bending of currents screening the applied positive field creates a region of negative field at the slit edge. Links: Baziljevich et al., Appl. Phys. Lett. 69, 3590 (1996).

 

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Bi-2223 tapes: rolling-induced defects Ag-sheathed (Bi,Pb)2Sr2Ca2Cu3O10 tapes fabricated using powder-in-tube method is today one of the most successful commercial HTS products (critical current up to 100A, length up to 1km). Magneto-optical imaging allows identification of typical defects in the tapes produced during the fabrication (rolling).

 

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Bi-2223 tapes: bending-induced defects Magneto-optical images demonstrate that bending of the tape causes cracks destroying the current flow. It allows determination of the critical bending strain. The images are taken in the remanent states after applying 0.1T field. Links: Koblischka et al., Supercond. Sci. Technol. 10, 693 (1997).

 

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Phenomena in Superconductors

 

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Melting transition in the vortex lattice At the melting transition the lattice of Abrikosov vortices transforms into a vortex line liquid or gas of vortex pancakes. The density of the vortices then changes discontinuously (by only a fraction of Gauss), which allows visualization of the transition by magneto-optical imaging. Image: Weizmann Superconductivity Lab Links: Visualization of the first-order vortex-lattice melting transition in a Bi-2212 crystal with movies @ Weizmann Superconductivity Lab

 

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Dendritic flux avalanches At low temperatures some superconducting films exhibit a thermo-magnetic instability resulting in highly unusual flux distributions. Dendritic flux structures seen on the image abruptly penetrate the film in response to slowly increasing applied field.   Links:     Dendritic instability in MgB2 films with numerous images and movies @ Oslo Lab

 

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Decoration of Josephson vortices by pancake vortices In strongly anistropic superconductors, e.g. in BSCCO, placed in a tilted magnetic field, two crossing vortex lattices co-exist: Josephson vortices and pancake vortices. The two kinds of vortices are attracted to each other. By imaging chains of pancake vortices on the superconductor surface, one can detect Josephson vortices behind it and study their migration between neighbouring stacks and transitions between different configurations. Image: V. K. Vlasko-Vlasov et al., Phys. Rev. B 66, 014523 (2002)

 

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Flux turbulence By subsequent application of positive and negative magnetic field one can create in a superconductor regions of flux with opposite polarity. The boundary between flux and antiflux (black line on the image) can display turbulent behavior characterized by an irregular propagation of finger-like patterns. Links: Macroturbulence page @ Oslo Lab

 

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Advanced methods

 

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Resolving individual vortices Though usual magneto-optical image shows distribution of "average" flux density, it is possible to push the resolution limit so that individual flux quanta can be seen. Each white spot on the image corresponds to a single vortex carrying one quantum of magnetic flux. Links: Single-vortex magneto-optics with movies of vortex dynamics @ Oslo Lab

 

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Calculation of current distribution The current density and magnetic field distributions are related to each other via Ampere's law. By inversion Ampere's law one can obtain the whole picture of current streamlines in a superconductor from its magneto-optical image. Links: Johansen et al., Phys. Rev. B 54, 16264 (1996) - 1D inversion in a YBCO strip Wijngaarden et al., Physica C 295, 177 (1998) - fast algorithm for 2D inversion Jooss et al., Rep. Prog. Phys. 65, 651 (2002) - review of inversion schemes

 

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Calculation of electric field distribution Variation of magnetic field with time is related to electric field via Maxwell's equation. From a time series of magneto-optical images one can calculate distribution of electric field in the superconductor. The image shows such distributions for a YBCO film with a grain boundary. Links: Giller et al., Phys. Rev. B 57, 14080 (1998) - 1D electric field profile Jooss et al., Phys. Rev. B 73, 094508 (2006) - 2D electric field distribution (some formulas in this paper are incorrect) Image: Jooss et al., Phys. Rev. B 65, 014505 (2002).

 

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Literature:

1. NATO Science Series: ”Magneto-Optical Imaging”
   Eds. T.H.Johansen and D.V.Shantsev
   Kluwer Academic Publishers
   Proceedings of the NATO Advanced Research Workshop on Magneto-Optical Imaging, 28-30 August 2003, Øystese, Norway
2. Magneto-optical studies of current distributions in high-Tc superconductors
   Ch. Jooss, J. Albrecht, H. Kuhn, S. Leonhardt and H. Kronmueller
   Rep. Prog. Phys. 65 (2002) 651-788

    

3. Magneto-optical investigations of superconductors
   M. R. Koblischka and R. J. Wijngaarden,
   Supercond. Sci. Technol. 8 (1995) 199-213

    

4. Vizualisation of magnetic flux in magnetic material and high temperature superconductors using farady effect in ferrimagnetic garnet films
   Polyanskii, A. A., Cai, X. Y., Feldmann, D. M. and Larbalestier, D. C.,
   Nano-crystalline and Thin Film Magnetic Oxides (NATO Science Series 3, High Technology 72) eds. I. Nedkov and M. Ausloos (Kluwer Academic Publishers: Netherlands) p. 353-370.