A. Forkl

Current density and magnetic field distribution in hard thin film superconductors

Abstract In thin film superconductors with magnetic fields applied perpendicular to the film plane, demagnetization effects lead to strong deviations of the flux density distribution B ( r ) from the predictions of the conventional critical state model. In particular if the magnetization M is taken as a probe for the critical current density j c of a thin film, the radial stray field component B r parallel to the film plane has to be taken into consideration. Especially in thin circular films with thicknesses lower than the London penetration depth, λ, the circular critical current density, jc=1/μ0(∂Bz/∂B−∂Bz/∂r), is determined by the gradient ∂Br/∂z rather than by ∂Bz/∂r. Using Bz(r)-data, measured by means of the magneto-optical Faraday effect on c-axis oriented YBa2Cu3O7−δ-films, we perform a selfconsistent calculation of the radial component Br(r), of the magnetic induction as well as of the current density distribution, jc(r), and the volume pinning force, fp.

High-resolution magneto-optical imaging of critical currents in YBa2Cu3O7−δ thin films

Abstract Magneto-optical investigation of flux penetration into type-II superconductors allows the determination of the local critical current density j c by inversion of the Biot–Savart law. Due to the required computational effort, in the past, this method was limited to low spatial resolution of the current density. In this paper, we present a fast inversion scheme using Fast-Fourier-Transformation, which allows high spatial resolution imaging of current distributions. Due to the nonlocal relation between magnetic field and current density, it is necessary to use a method that images field and current distribution of superconductors as a whole, and enables high resolution at the same time. To demonstrate the power of our method, the local current density in a YBa 2 Cu 3 O 7− δ square and disk are imaged with high resolution and described in detail for increasing and decreasing external magnetic fields. At low fields, the dependencies of j c ( B ) on the local magnetic field B and of the average j c (magnetic moment) on the applied magnetic field show significant differences. Finally, we directly image the local current density near macroscopic defects in a square and a disk. The observed current distributions near defects significantly differ from the predictions of an extended Bean model.

Thickness and roughness dependence of magnetic flux penetration and critical current densities in YBa2Cu3O7−δ thin films

Abstract As a result of the island growth mode all epitactic YBa 2 Cu 3 O 7−δ thin films show surface roughness. To investigate a possible surface pinning mechanism, combined magneto-optical and atomic force microscopy studies were carried out. Measurement of the spatial distribution of magnetic flux density on the surface of thin YBa 2 Cu 3 O 7−δ films by means of the magneto-optical Faraday effect (MOFE) under application of external magnetic fields allows an accurate determination of critical current densities j c . In order to have a quantitative comparison between the Bean model for thin films and experiment, a new nonlinear calibration technique for the flux densities was developed. For determining the thickness and roughness dependence of j c , samples with YBaCuO-strips of different thickness and roughness were patterned from one film. With the roughness determined experimentally by afm measurements, a satisfactory agreement between the measured and calculated thickness dependence of j c is achieved. Surface pinning is found to cause between 10%–30% of the critical current densities of epitactic YBa 2 Cu 3 O 7−δ thin films. Additionally microscopic deviations of the flux profiles from the Bean model are detected. Evidence for matching effects of the vortex line distribution with the density of surface pins is given.

Investigation of the mixed state of YBa2Cu3O7−δ superconductors

The magneto‐optical Faraday effect has been used to observe the penetration of magnetic flux into sintered YBa2 Cu3 O7−δ. In addition, measurements of the magnetic polarization are performed with a SQUID magnetometer. The magneto‐optical Faraday effect shows an inhomogeneous penetration of the magnetic flux into the sample. In a first step the flux penetrates into the intergranular regions and in a second step into single grains separately. A spatial gradient of the flux density within each grain is built up, indicating pinning forces. In the remanent state in each grain trapped flux is observed. The measured magnetization curves show good agreement with the magneto‐optical investigations of the flux penetration.The magneto-optical Faraday effect has been used to observe the penetration of magnetic flux into sintered YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}}. In addition, measurements of the magnetic polarization are performed with a SQUID magnetometer. The magneto-optical Faraday effect shows an inhomogeneous penetration of the magnetic flux into the sample. In a first step the flux penetrates into the intergranular regions and in a second step into single grains separately. A spatial gradient of the flux density within each grain is built up, indicating pinning forces. In the remanent state in each grain trapped flux is observed. The measured magnetization curves show good agreement with the magneto-optical investigations of the flux penetration.

Study of flux distributions in high-Tc single crystals and thin films using magneto-optic techniques

Abstract The current progress of magneto-optical techniques for direct investigations of magnetic flux structures in type-II superconductors with high spatial resolution is presented. Wide possibilities are offered by the high-resolution Faraday effect technique requiring a thin layer of EuSe as an indicator and the method using ferrimagnetic garnet films with in-plane anisotropy. The advantages of both methods are combined to investigate flux structures of an YBa 2 Cu 3 O 7 (YBCO) thin film partly irradiated with 25 MeV oxygen ions and for inhomogeneously twinned YBCO single crystals.

Temperature dependence of the domain structure in Fe14Nd2B single crystals during the spin-reorientation transition

Abstract The temperature dependence of the magnetic domain structure of Fe 14 Nd 2 B single crystals is investigated from room temperature down to 4.2 K by means of the magneto-optical Kerr effect. The parallel stripe domain structure characteristic of high-anisotropy uniaxial ferromagnets is observed on the ( h k 0) planes of the crystals at room temperature. This structure remains practically unchanged down to about 140 K. In the vicinity of the magnetic phase transition at T SR = 135 K the domain structure undergoes intense realignment. Below T SR a new type of domain structure occurs being characterized by a periodic modulation of the magnetization orientation inside the main domains together with a developed system of closure domains having different preferential orientations. For the particular sample studied the width of the main domains at 4.2 K is about 100 μm, while that of closure domains is about 2–5 μm.

Anisotropy of perpendicular field penetration into high-Tc superconductors induced by strong longitudinal field

Abstract The geometry of penetration of a magnetic field oriented perpendicular to the surface of a superconductor is changed by the presence of a longitudinal field. This is studied directly by means of the magneto-optical technique in different high-Tc materials. In YBa2Cu3O7 single crystals Brandts mode of magnetization is observed, namely, penetration of an AC field only along the longitudinal field even if the corresponding dimension of the sample is much longer than the other two. This anisotropy is the evidence that the force-free configuration of current and vortices cannot be destroyed by cutting and reconnection of the vortices in this 3D superconductor. On the contrary, the absence of the induced anisotropy in Bi2Sr2CaCu2O8 single crystals reveals the independence of pancake vortices in CuO layers from longitudinal field which makes a realization of the force-free configuration impossible in the layered 2D superconductor. An intermediate effect in thin films indicates that vortices are almost normal to the film surface even if the applied field is nearly parallel to it. The described experiment can be used as a new tool to study the internal vortex structure in superconductors.

A new calibration technique for the determination of magnetic flux density with the magneto-optical Faraday effect

Abstract Using the high resolution magneto-optical Faraday effect the magnetic flux density distribution of circular shaped Y1Ba2Cu3O7−x thin films is investigated. A new calibration technique is developed to determine the z-component Bz(x,y) of the local magnetic flux density B (x,y) in the x,y-surface of the films with high accuracy. The observed flux density profiles agree well with calculations of B ( r ) using a simple model with homogeneous current distribution. The appearance of a negative magnetic flux and reversed flux lines at the edge of the films in the remanent state is caused by stray fields of the trapped flux. For a determination of the local critical current density jc, the local pinning forces pv and the magnetization of thin films from the observed magnetic flux density distribution B (x,y) the curvature of the magnetic field ∂Bz/∂r and ∂Br/∂z, respectively, has to be taken into account.

Law of approach to magnetic saturation in inhomogeneous ferri- and antiferromagnets and in amorphous iron-rich Fe-Zr alloys

Abstract The magnetization curve of a two-phase two-sublattice model is calculated analytically. In one phase a ferromagnetic coupling is assumed which contributes to the total magnetization whereas in the other phase a ferrimagnetic interaction takes place. Within the framework of a molecular field theory the magnetization curve of this ferrimagnetic phase is calculated assuming a certain distribution of the molecular field interactions. The law of approach to magnetic saturation yields for the leading term a H −1 -dependence in contrast to fluctuations of the local magnetic anisotropy which in general yield a H − built1 2 -law. The calculations of the two-phase two-sublattice model agree well with measurements of the high-field magnetization curve of amorphous Fe 1− x Zr x -alloys with 0.076 ≤ x ≤ 0.11 showing that with decreasing Zr-content an increase of the ferrimagnetic phase exists.

A new method to determine the critical current density of superconducting thin films based on magneto-optic measurements

Abstract Direct observation and measurement of the spatial flux density distribution on the surface of Y 1 Ba 2 Cu 3 O 7- x superconducting thin films under application of an external magnetic field are performed using magneto-optical EuS/EuF 2 and iron-garnet indicators. A new, very accurate method to determine the critical current density of stripe-structured thin films is presented, based on a recent theory for flux penetration in superconducting thin films.