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Equilibrium topology of the intermediate state in type-I superconductors of different shapes

Ruslan Prozorov

Ames Laboratory and Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011

Submitted: November 2006
Published: June 2007


High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric barrier that results in a topological hysteresis -- flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region. It is concluded that flux tubes represent the equilibrium topology of the intermediate state in reversible samples, whereas laminar structure appears in samples with magnetic hysteresis (either bulk or geometric).

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Disc - shaped Pb single crystal

Disc diameter 5 mm and thickness 1 mm. Four different crystals wever measured. With different orientation - (100) and (111) - no difference was detected.

Flux penetration and exit after cooling in zero field. (111) - oriented crystal

Flux penetration and exit after cooling in zero field. (100) - oriented crystal

Penetration of the normal component of the field superimposed on a constant parallel (to a disc surface) field H=100 Oe.

Magnetic field is rotated around the vertical axis (not precision control of the angle was attempted)

Pb hemisphere

Diameter 4 mm . Made by casting of 99.999% lead under inert atmosphere into a mold. Subsequent polishing and vacuum annealing reduced residual pinning even further.
Some fuzzy structure just over the edge is small amount of leftover lead.

Penetration and exit of the magnetic field. (defects are mostly on the indicator film and some surface scratches)

Warming from T= 3.8 K with H=200 Oe applied after cooling in zero field

Another Pb sphere



The tubes are clearly seen both on penetration and exit


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