Experimental Study of the Magnetic Field Distribution and Shape of Domains Near the Surface of a Type-I Superconductor i
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ORIGINAL PAPER
Experimental Study of the Magnetic Field Distribution and Shape of Domains Near the Surface of a Type-I Superconductor in the Intermediate State V. Kozhevnikov1
· A. Suter2 · T. Prokscha2 · C. Van Haesendonck3
Received: 18 April 2020 / Accepted: 12 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The importance of accounting for the inhomogeneity of the magnetic field distribution and roundness of domain walls near the surface of type-I superconductors in the intermediate state for forming the equilibrium flux structure was predicted by Landau eight decades ago. Further studies confirmed this prediction and extended it to all equilibrium properties of this state. Here we report on direct depth-resolved measurements of the field distribution and shape of domains near the surface of high-purity type-I (indium) films in a perpendicular field using Low-Energy Muon Spin Rotation spectroscopy. We find that at low applied fields (in about half of the field range of the intermediate state) the field distribution and domains’ shape agrees with that proposed by Tinkham. However, for high fields our data suggest that reality differs from theoretical expectations. In particular, the width of the superconducting laminae can expand near the surface leading to formation of a maximum in the static magnetic field in the current-free space outside the sample. A possible interpretation of these experimental results is discussed. Keywords Superconductivity · Type-I superconductors · Intermediate state · Muon spin rotation spectroscopy · Magnmetic domains · Near-surface magnetic field distribution
1 Introduction The intermediate state (IS) in type-I superconductors is a classical example of a thermodynamically equilibrium systems with spatially modulated phases, where a continuous medium is split into domains of different phases. Such systems with strikingly similar domain patterns are known in a broad variety of physical-chemical formations, in which the pattern constitutes due to competition between various energy contributions in the system free energy [1]. The relative simplicity in tuning the domain separation (period of the domain structure) in the IS by varying the applied magnetic field and/or temperature, makes the IS a unique and very interesting object for studies of such systems. Recently, V. Kozhevnikov
[email protected] 1
Tulsa Community College, Tulsa, OK 74119, USA
2
Paul Scherrer Institut, 5232 Villigen, Switzerland
3
Solid State Physics and Magnetism Section, KU Leuven, 3001 Leuven, Belgium
being attracted by the beauty of domain patterns (see, e.g., [2–4]) and long-standing challenges of the IS physics [5–7], some of us revisited the problem of the IS experimentally. This resulted in the development of a new theoretical model, which consistently addresses properties of the IS in samples of a planar geometry [8, 9]. Simultaneously, this study made clear the important role of surface-related properties for forming equilibrium characteristics
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